Abstract Some trace inequalities of Shisha-Mond type for operators in Hilbert spaces are provided. Applications in connection to Grüss inequality and for convex functions of selfadjoint operators are also given.
{"title":"Trace inequalities of Shisha-Mond type for operators in Hilbert spaces","authors":"S. Dragomir","doi":"10.1515/conop-2017-0004","DOIUrl":"https://doi.org/10.1515/conop-2017-0004","url":null,"abstract":"Abstract Some trace inequalities of Shisha-Mond type for operators in Hilbert spaces are provided. Applications in connection to Grüss inequality and for convex functions of selfadjoint operators are also given.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"4 1","pages":"32 - 47"},"PeriodicalIF":0.6,"publicationDate":"2017-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2017-0004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43426302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this note, we improve the idea of the Tsallis entropy in a complex domain. This improvement is contingent on the fractional operator in a complex domain (type Alexander). We clarify some new classes of analytic functions, which are planned in view of the geometry function theory. This category of entropy is called fractional entropy; accordingly, we demand them fractional entropic geometry classes. Other geometric properties are established in the sequel. Our exhibition is supported by the Maxwell Lemma and Jack Lemma.
{"title":"On a class of analytic functions generated by fractional integral operator","authors":"R. Ibrahim","doi":"10.1515/conop-2017-0001","DOIUrl":"https://doi.org/10.1515/conop-2017-0001","url":null,"abstract":"Abstract In this note, we improve the idea of the Tsallis entropy in a complex domain. This improvement is contingent on the fractional operator in a complex domain (type Alexander). We clarify some new classes of analytic functions, which are planned in view of the geometry function theory. This category of entropy is called fractional entropy; accordingly, we demand them fractional entropic geometry classes. Other geometric properties are established in the sequel. Our exhibition is supported by the Maxwell Lemma and Jack Lemma.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"4 1","pages":"1 - 6"},"PeriodicalIF":0.6,"publicationDate":"2017-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2017-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49368317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Let Ω be an open simply connected proper subset of the complex plane and φ an analytic self map of Ω. If f is in the Hardy-Smirnov space defined on Ω, then the operator that takes f to f º φ is a composition operator. We show that for any Ω, analytic self maps that induce bounded Hermitian composition operators are of the form Φ(w) = aw + b where a is a real number. For ceratin Ω, we completely describe values of a and b that induce bounded Hermitian composition operators.
{"title":"Hermitian composition operators on Hardy-Smirnov spaces","authors":"Gajath Gunatillake","doi":"10.1515/conop-2017-0002","DOIUrl":"https://doi.org/10.1515/conop-2017-0002","url":null,"abstract":"Abstract Let Ω be an open simply connected proper subset of the complex plane and φ an analytic self map of Ω. If f is in the Hardy-Smirnov space defined on Ω, then the operator that takes f to f º φ is a composition operator. We show that for any Ω, analytic self maps that induce bounded Hermitian composition operators are of the form Φ(w) = aw + b where a is a real number. For ceratin Ω, we completely describe values of a and b that induce bounded Hermitian composition operators.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"4 1","pages":"17 - 7"},"PeriodicalIF":0.6,"publicationDate":"2017-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2017-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49496058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper we consider the map L defined on the Bergman space La2(+) $L_a^2({{rmmathbb{C}}_{rm{ + }}})$ of the right half plane ℂ+ by (Lf)(w)=πM′(w)∫+(fM′)(s)|bw(s)|2dA˜(s) $(Lf)(w) = pi M'(w)intlimits_{{{rmmathbb{C}}_{rm{ + }}}} {left( {{f over {M'}}} right)} (s){left| {{b_w}(s)} right|^2}dtilde A(s)$ where bw¯(s)=1π1+w1+w2Rew(s+w)2 ${b_{bar w}}(s) = {1 over {sqrt pi }}{{1 + w} over {1 + w}}{{2{mathop{Re}nolimits} w} over {{{(s + w)}^2}}}$ , s ∈ ℂ+ and Ms=1-s1+s $Ms = {{1 - s} over {1 + s}}$ . We show that L commutes with the weighted composition operators Wa, a ∈ 𝔻 defined on La2(+) $L_a^2({{rmmathbb{C}}_{rm{ + }}})$ , as Waf=(f∘ta)M′M′∘ta ${W_a}f = (f circ {t_a}){{M'} over {M' circ {t_a}}}$ , f∈La2(+) $f in L_a^2(mathbb{C_ + })$ . Here ta(s)=-ids+(1-c)(1+c)s+id $${t_a}(s) = {{ - ids + (1 - c)} over {(1 + c)s + id}} , if a = c + id ∈ 𝔻 c, d ∈ ℝ. For a ∈ 𝔻, define Va:La2(+)→La2(+) ${V_a}:L_a^2({{mathbb{C}}_{rm{ + }}}) to L_a^2({{mathbb{C}}_{rm{ + }}})$ by (Vag)(s) = (g∘ta)(s)la(s) where la(s)=1-|a|2((1+c)s+id)2 $la(s) = {{1 - {{left| a right|}^2}} over {{{((1 + c)s + id)}^2}}}$ .We look at the action of the class of unitary operators Va, a ∈ 𝔻 on the linear operator L. We establish that Lˆ = L where L⌢=∫𝔻VaLVadA(a) $mathord{buildrel{lower3pthbox{$scriptscriptstylefrown$}}over L} = intlimits_{mathbb{D}} {{V_a}L{V_a}dA(a)}$ and dA is the area measure on 𝔻. In fact the map L satisfies the averaging condition L˜(w1)=∫DL˜(ta¯(w1))dA(a),for all w1∈C+ $$tilde L({w_1}) = intlimits_{mathbb{D}} {tilde L({t_{bar a}}({w_1}))dA(a),{rm{for all }}{w_1} in {{rm{C}}_{rm{ + }}}}$$ where L˜(w1)=〈Lbw¯1,bw¯1〉 $tilde L({w_1}) = leftlangle {L{b_{{{bar w}_1}}},{b_{{{bar w}_1}}}} rightrangle$.
{"title":"A Berezin-type map and a class of weighted composition operators","authors":"N. Das","doi":"10.1515/conop-2017-0003","DOIUrl":"https://doi.org/10.1515/conop-2017-0003","url":null,"abstract":"Abstract In this paper we consider the map L defined on the Bergman space La2(+) $L_a^2({{rmmathbb{C}}_{rm{ + }}})$ of the right half plane ℂ+ by (Lf)(w)=πM′(w)∫+(fM′)(s)|bw(s)|2dA˜(s) $(Lf)(w) = pi M'(w)intlimits_{{{rmmathbb{C}}_{rm{ + }}}} {left( {{f over {M'}}} right)} (s){left| {{b_w}(s)} right|^2}dtilde A(s)$ where bw¯(s)=1π1+w1+w2Rew(s+w)2 ${b_{bar w}}(s) = {1 over {sqrt pi }}{{1 + w} over {1 + w}}{{2{mathop{Re}nolimits} w} over {{{(s + w)}^2}}}$ , s ∈ ℂ+ and Ms=1-s1+s $Ms = {{1 - s} over {1 + s}}$ . We show that L commutes with the weighted composition operators Wa, a ∈ 𝔻 defined on La2(+) $L_a^2({{rmmathbb{C}}_{rm{ + }}})$ , as Waf=(f∘ta)M′M′∘ta ${W_a}f = (f circ {t_a}){{M'} over {M' circ {t_a}}}$ , f∈La2(+) $f in L_a^2(mathbb{C_ + })$ . Here ta(s)=-ids+(1-c)(1+c)s+id $${t_a}(s) = {{ - ids + (1 - c)} over {(1 + c)s + id}} , if a = c + id ∈ 𝔻 c, d ∈ ℝ. For a ∈ 𝔻, define Va:La2(+)→La2(+) ${V_a}:L_a^2({{mathbb{C}}_{rm{ + }}}) to L_a^2({{mathbb{C}}_{rm{ + }}})$ by (Vag)(s) = (g∘ta)(s)la(s) where la(s)=1-|a|2((1+c)s+id)2 $la(s) = {{1 - {{left| a right|}^2}} over {{{((1 + c)s + id)}^2}}}$ .We look at the action of the class of unitary operators Va, a ∈ 𝔻 on the linear operator L. We establish that Lˆ = L where L⌢=∫𝔻VaLVadA(a) $mathord{buildrel{lower3pthbox{$scriptscriptstylefrown$}}over L} = intlimits_{mathbb{D}} {{V_a}L{V_a}dA(a)}$ and dA is the area measure on 𝔻. In fact the map L satisfies the averaging condition L˜(w1)=∫DL˜(ta¯(w1))dA(a),for all w1∈C+ $$tilde L({w_1}) = intlimits_{mathbb{D}} {tilde L({t_{bar a}}({w_1}))dA(a),{rm{for all }}{w_1} in {{rm{C}}_{rm{ + }}}}$$ where L˜(w1)=〈Lbw¯1,bw¯1〉 $tilde L({w_1}) = leftlangle {L{b_{{{bar w}_1}}},{b_{{{bar w}_1}}}} rightrangle$.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"4 1","pages":"18 - 31"},"PeriodicalIF":0.6,"publicationDate":"2017-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2017-0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47193947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic functions with values in a Banach space.
{"title":"Vector-valued holomorphic and harmonic functions","authors":"W. Arendt","doi":"10.1515/conop-2016-0007","DOIUrl":"https://doi.org/10.1515/conop-2016-0007","url":null,"abstract":"Abstract Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic functions with values in a Banach space.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"3 1","pages":"68 - 76"},"PeriodicalIF":0.6,"publicationDate":"2016-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2016-0007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66888134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract If H denotes a Hilbert space of analytic functions on a region Ω ⊆ Cd , then the weak product is defined by We prove that if H is a first order holomorphic Besov Hilbert space on the unit ball of Cd , then the multiplier algebras of H and of H ⊙ H coincide.
{"title":"A remark on the multipliers on spaces of Weak Products of functions","authors":"S. Richter, B. Wick","doi":"10.1515/conop-2016-0004","DOIUrl":"https://doi.org/10.1515/conop-2016-0004","url":null,"abstract":"Abstract If H denotes a Hilbert space of analytic functions on a region Ω ⊆ Cd , then the weak product is defined by We prove that if H is a first order holomorphic Besov Hilbert space on the unit ball of Cd , then the multiplier algebras of H and of H ⊙ H coincide.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"3 1","pages":"25 - 28"},"PeriodicalIF":0.6,"publicationDate":"2016-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2016-0004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66888361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea [30, 31] for the operator are obtained. As a consequence, some sufficient conditions for the boundedness of Min the two weight setting in the spirit of the results obtained by C. Pérez and E. Rela [26] and very recently by M. Lacey and S. Spencer [17] for the Hardy-Littlewood maximal operator are derived. As a byproduct some new quantitative estimates for the Poisson integral are obtained.
{"title":"A quantitative approach to weighted Carleson condition","authors":"I. Rivera-Ríos","doi":"10.1515/conop-2017-0006","DOIUrl":"https://doi.org/10.1515/conop-2017-0006","url":null,"abstract":"Abstract Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea [30, 31] for the operator are obtained. As a consequence, some sufficient conditions for the boundedness of Min the two weight setting in the spirit of the results obtained by C. Pérez and E. Rela [26] and very recently by M. Lacey and S. Spencer [17] for the Hardy-Littlewood maximal operator are derived. As a byproduct some new quantitative estimates for the Poisson integral are obtained.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"4 1","pages":"58 - 75"},"PeriodicalIF":0.6,"publicationDate":"2016-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2017-0006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66888720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Let α > 0. By Cα we mean the terraced matrix defined by if 1 ≤ k ≤ n and 0 if k > n. In this paper, we show that a necessary and sufficient condition for the induced operator on lp, to be p-summing, is α > 1; 1 ≤ p < ∞. When the more general terraced matrix B, defined by bnk = βn if 1 ≤ k ≤ n and 0 if k > n, is considered, the necessary and sufficient condition turns out to be in the region 1/p + 1/q ≤ 1.
{"title":"Absolutely Summing Terraced Matrices","authors":"Ibrahim Almasri","doi":"10.1515/conop-2016-0001","DOIUrl":"https://doi.org/10.1515/conop-2016-0001","url":null,"abstract":"Abstract Let α > 0. By Cα we mean the terraced matrix defined by if 1 ≤ k ≤ n and 0 if k > n. In this paper, we show that a necessary and sufficient condition for the induced operator on lp, to be p-summing, is α > 1; 1 ≤ p < ∞. When the more general terraced matrix B, defined by bnk = βn if 1 ≤ k ≤ n and 0 if k > n, is considered, the necessary and sufficient condition turns out to be in the region 1/p + 1/q ≤ 1.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"3 1","pages":"1 - 7"},"PeriodicalIF":0.6,"publicationDate":"2016-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2016-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66887736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract For operators generated by a certain class of infinite three-diagonal matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying second order finite-difference equations. This enables us to describe some asymptotic behavior of the corresponding systems of vector orthogonal polynomials on the resolvent set. We also find that the operators generated by infinite Jacobi matrices have the largest resolvent set in this class.
{"title":"A study of resolvent set for a class of band operators with matrix elements","authors":"A. Osipov","doi":"10.1515/conop-2016-0010","DOIUrl":"https://doi.org/10.1515/conop-2016-0010","url":null,"abstract":"Abstract For operators generated by a certain class of infinite three-diagonal matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying second order finite-difference equations. This enables us to describe some asymptotic behavior of the corresponding systems of vector orthogonal polynomials on the resolvent set. We also find that the operators generated by infinite Jacobi matrices have the largest resolvent set in this class.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"3 1","pages":"85 - 93"},"PeriodicalIF":0.6,"publicationDate":"2016-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2016-0010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66888404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Operators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.
形式为C h f = f°h的函数空间上的算子，其中h是一个固定映射，称为带符号h的复合算子。我们研究了作用于右半平面上的Hilbert Hardy空间上的这类算子，并描述了它们可逆、Fredholm、酉和厄米的情形。我们用inner和Möbius符号分别确定普通复合运算符。在选定的情况下，我们计算它们的光谱、基本光谱和数值范围。
{"title":"Invertible and normal composition operators on the Hilbert Hardy space of a half–plane","authors":"Valentin Matache","doi":"10.1515/conop-2016-0009","DOIUrl":"https://doi.org/10.1515/conop-2016-0009","url":null,"abstract":"Abstract Operators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"3 1","pages":"77 - 84"},"PeriodicalIF":0.6,"publicationDate":"2016-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2016-0009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66888283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：