In this paper, we introduce and investigate multi subspacehypercyclic operators and prove that multi-hypercyclic operators are multi subspace-hypercyclic. We show that if T is M -hypercyclic or multi M -hypercyclic, then Tn is multi M -hypercyclic for any natural number n and by using this result, make some examples of multi subspacehypercyclic operators. We prove that multi M -hypercyclic operators have somewhere dense orbits in M . We show that analytic Toeplitz operators can not be multi subspace-hypercyclic. Also, we state a sufficient condition for coanalytic Toeplitz operators to be multi subspace-hypercyclic.
{"title":"On multi subspace-hypercyclic operators","authors":"M. Moosapoor","doi":"10.4134/CKMS.C200118","DOIUrl":"https://doi.org/10.4134/CKMS.C200118","url":null,"abstract":"In this paper, we introduce and investigate multi subspacehypercyclic operators and prove that multi-hypercyclic operators are multi subspace-hypercyclic. We show that if T is M -hypercyclic or multi M -hypercyclic, then Tn is multi M -hypercyclic for any natural number n and by using this result, make some examples of multi subspacehypercyclic operators. We prove that multi M -hypercyclic operators have somewhere dense orbits in M . We show that analytic Toeplitz operators can not be multi subspace-hypercyclic. Also, we state a sufficient condition for coanalytic Toeplitz operators to be multi subspace-hypercyclic.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70438297","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}
{"title":"CONJUGACY INVARIANTS OF QUATERNION MATRICES","authors":"Joonhyun Kim, Qianghua Luo","doi":"10.4134/CKMS.C200089","DOIUrl":"https://doi.org/10.4134/CKMS.C200089","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70438498","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}
Let R be a commutative ring with unity. The extension of annihilating-ideal graph of R, AG(R), is the graph whose vertices are nonzero annihilating ideals of R and two distinct vertices I and J are adjacent if and only if there exist n,m ∈ N such that InJm = (0) with In, Jm 6= (0). First, we differentiate when AG(R) and AG(R) coincide. Then, we have characterized the diameter and the girth of AG(R) when R is a finite direct products of rings. Moreover, we show that AG(R) contains a cycle, if AG(R) 6= AG(R).
设R是一个有单位的交换环。R的湮灭理想图AG(R)的扩展是顶点为R的非零湮灭理想且两个不同的顶点I和J相邻的图，当且仅当n,m∈n使得InJm =(0)与In, Jm 6=(0)。首先，我们区分AG(R)与AG(R)重合的情况。然后，我们刻画了当R是环的有限直积时AG(R)的直径和周长。此外，我们证明了AG(R)包含一个环，如果AG(R) 6= AG(R)。
{"title":"AN EXTENSION OF ANNIHILATING-IDEAL GRAPH OF COMMUTATIVE RINGS","authors":"Mahtab Koohi Kerahroodi, Fatemeh Nabaei","doi":"10.4134/CKMS.C200006","DOIUrl":"https://doi.org/10.4134/CKMS.C200006","url":null,"abstract":"Let R be a commutative ring with unity. The extension of annihilating-ideal graph of R, AG(R), is the graph whose vertices are nonzero annihilating ideals of R and two distinct vertices I and J are adjacent if and only if there exist n,m ∈ N such that InJm = (0) with In, Jm 6= (0). First, we differentiate when AG(R) and AG(R) coincide. Then, we have characterized the diameter and the girth of AG(R) when R is a finite direct products of rings. Moreover, we show that AG(R) contains a cycle, if AG(R) 6= AG(R).","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70438120","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}
We consider the weighted spaces `p(S, φ) and `p(S, ψ) for 1 < p < +∞, where φ and ψ are weights on S (= N or Z). We obtain a sufficient condition for `p(S, ψ) to be multiplier weighted-space of `p(S, φ) and `p(S, ψ). Our condition characterizes the last multiplier weightedspace in the case where S = Z. As a consequence, in the particular case where ψ = φ, the weighted space `p(Z,ψ) is a convolutive algebra. 1. Preliminaries and introduction Let S (S = N or S = Z) and p ∈ ]1,+∞[. We say that ω is a weight on S if ω : S −→ [1,+∞[, is a map satisfying: ∑ n∈S ω(n) 1 1−p < +∞. We consider the weighted space: `(S, ω) = { (a(n))n∈S ∈ C S : ∑ n∈S |a(n)| ω(n) < +∞ } . Endowed with the norm |·|p,ω defined by: |a|p,ω = (∑ n∈S |a(n)| ω(n) ) 1 p for every (a(n))n∈S ∈ ` (S, ω), the space `(S,ω) becomes a Banach subspace of ` (S). We say that the weight ω is m-convolutive if a positive constant γ = γ(ω) exists such that: ω 1 1−p ∗ ω 1 1−p ≤ γ ω 1 1−p , where ∗ denotes the convolution product. If a= (a(n))n∈S ∈ `(S, ω), we define the complex function F(a) by F(a)(t) = ∑ n∈S a(n)e for every t ∈ R. Received February 6, 2020; Revised April 8, 2020; Accepted July 2, 2020. 2010 Mathematics Subject Classification. 46J10, 46H30.
{"title":"ON MULTIPLIER WEIGHTED-SPACE OF SEQUENCES","authors":"L. Bouchikhi, A. Kinani","doi":"10.4134/CKMS.C200040","DOIUrl":"https://doi.org/10.4134/CKMS.C200040","url":null,"abstract":"We consider the weighted spaces `p(S, φ) and `p(S, ψ) for 1 < p < +∞, where φ and ψ are weights on S (= N or Z). We obtain a sufficient condition for `p(S, ψ) to be multiplier weighted-space of `p(S, φ) and `p(S, ψ). Our condition characterizes the last multiplier weightedspace in the case where S = Z. As a consequence, in the particular case where ψ = φ, the weighted space `p(Z,ψ) is a convolutive algebra. 1. Preliminaries and introduction Let S (S = N or S = Z) and p ∈ ]1,+∞[. We say that ω is a weight on S if ω : S −→ [1,+∞[, is a map satisfying: ∑ n∈S ω(n) 1 1−p < +∞. We consider the weighted space: `(S, ω) = { (a(n))n∈S ∈ C S : ∑ n∈S |a(n)| ω(n) < +∞ } . Endowed with the norm |·|p,ω defined by: |a|p,ω = (∑ n∈S |a(n)| ω(n) ) 1 p for every (a(n))n∈S ∈ ` (S, ω), the space `(S,ω) becomes a Banach subspace of ` (S). We say that the weight ω is m-convolutive if a positive constant γ = γ(ω) exists such that: ω 1 1−p ∗ ω 1 1−p ≤ γ ω 1 1−p , where ∗ denotes the convolution product. If a= (a(n))n∈S ∈ `(S, ω), we define the complex function F(a) by F(a)(t) = ∑ n∈S a(n)e for every t ∈ R. Received February 6, 2020; Revised April 8, 2020; Accepted July 2, 2020. 2010 Mathematics Subject Classification. 46J10, 46H30.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70438489","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}
{"title":"PSEUDO-HERMITIAN 2-TYPE LEGENDRE SURFACES IN THE UNIT SPHERE S 5","authors":"Ji-Eun Lee","doi":"10.4134/CKMS.C180530","DOIUrl":"https://doi.org/10.4134/CKMS.C180530","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70436440","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}
In this paper we consider Lk-conjecture introduced in [5, 6] for hypersurface Mn in space form Rn+1(c) with three principal curvatures. When c = 0,−1, we show that every L1-biharmonic hypersurface with three principal curvatures and H1 is constant, has H2 = 0 and at least one of the multiplicities of principal curvatures is one, where H1 and H2 are first and second mean curvature of M and we show that there is not L2-biharmonic hypersurface with three disjoint principal curvatures and, H1 and H2 is constant. For c = 1, by considering having three principal curvatures, we classify L1-biharmonic hypersurfaces with multiplicities greater than one, H1 is constant and H2 = 0, proper L1-biharmonic hypersurfaces which H1 is constant, and L2-biharmonic hypersurfaces which H1 and H2 is constant.
{"title":"L K -BIHARMONIC HYPERSURFACES IN SPACE FORMS WITH THREE DISTINCT PRINCIPAL CURVATURES","authors":"M. Aminian","doi":"10.4134/CKMS.C200056","DOIUrl":"https://doi.org/10.4134/CKMS.C200056","url":null,"abstract":"In this paper we consider Lk-conjecture introduced in [5, 6] for hypersurface Mn in space form Rn+1(c) with three principal curvatures. When c = 0,−1, we show that every L1-biharmonic hypersurface with three principal curvatures and H1 is constant, has H2 = 0 and at least one of the multiplicities of principal curvatures is one, where H1 and H2 are first and second mean curvature of M and we show that there is not L2-biharmonic hypersurface with three disjoint principal curvatures and, H1 and H2 is constant. For c = 1, by considering having three principal curvatures, we classify L1-biharmonic hypersurfaces with multiplicities greater than one, H1 is constant and H2 = 0, proper L1-biharmonic hypersurfaces which H1 is constant, and L2-biharmonic hypersurfaces which H1 and H2 is constant.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70438654","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}
S. Iqbal, J. Pečarić, M. Samraiz, Hassan Tehmeena, Z. Tomovski
{"title":"ON SOME WEIGHTED HARDY-TYPE INEQUALITIES INVOLVING EXTENDED RIEMANN-LIOUVILLE FRACTIONAL CALCULUS OPERATORS","authors":"S. Iqbal, J. Pečarić, M. Samraiz, Hassan Tehmeena, Z. Tomovski","doi":"10.4134/CKMS.C180458","DOIUrl":"https://doi.org/10.4134/CKMS.C180458","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70436447","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}
{"title":"SHECHTER SPECTRA AND RELATIVELY DEMICOMPACT LINEAR RELATIONS","authors":"A. Ammar, S. Fakhfakh, A. Jeribi","doi":"10.4134/CKMS.C190021","DOIUrl":"https://doi.org/10.4134/CKMS.C190021","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70436569","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}
{"title":"IDEALIZATION OF EM-HERMITE RINGS","authors":"Hiba Abdelkarim, Emad Abuosba, Manal Ghanem","doi":"10.4134/CKMS.C180477","DOIUrl":"https://doi.org/10.4134/CKMS.C180477","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70436686","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}
Let R be a commutative ring with unity, A and B be Ralgebras, M be a (A,B)-bimodule and N be a (B,A)-bimodule. The Ralgebra S = S(A,M,N,B) is a generalized matrix algebra defined by the Morita context (A,B,M,N, ξMN,ΩNM). In this article, we study generalized derivation and generalized Jordan derivation on generalized matrix algebras and prove that every generalized Jordan derivation can be written as the sum of a generalized derivation and antiderivation with some limitations. Also, we show that every generalized Jordan derivation is a generalized derivation on trivial generalized matrix algebra over a field.
{"title":"ON GENERALIZED JORDAN DERIVATIONS OF GENERALIZED MATRIX ALGEBRAS","authors":"M. Ashraf, A. Jabeen","doi":"10.4134/CKMS.C190362","DOIUrl":"https://doi.org/10.4134/CKMS.C190362","url":null,"abstract":"Let R be a commutative ring with unity, A and B be Ralgebras, M be a (A,B)-bimodule and N be a (B,A)-bimodule. The Ralgebra S = S(A,M,N,B) is a generalized matrix algebra defined by the Morita context (A,B,M,N, ξMN,ΩNM). In this article, we study generalized derivation and generalized Jordan derivation on generalized matrix algebras and prove that every generalized Jordan derivation can be written as the sum of a generalized derivation and antiderivation with some limitations. Also, we show that every generalized Jordan derivation is a generalized derivation on trivial generalized matrix algebra over a field.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70437782","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}
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