Pub Date : 2023-12-16DOI: 10.1007/s11117-023-01009-0
S. Dempe, N. Gadhi, L. Lafhim
{"title":"Correction to: Optimality conditions for pessimistic bilevel problems using convexificator","authors":"S. Dempe, N. Gadhi, L. Lafhim","doi":"10.1007/s11117-023-01009-0","DOIUrl":"https://doi.org/10.1007/s11117-023-01009-0","url":null,"abstract":"","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138995640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-27DOI: 10.1007/s11117-023-01021-4
Bahri Turan, Hüma Gürkök
Let E and F be two Archimedean Riesz spaces. An operator (T:Erightarrow F) is said to be unbounded order continuous (uo-continuous), if (u_{alpha }overset{uo}{rightarrow }0) in E implies (Tu_{alpha }overset{uo}{ rightarrow }0) in F. In this study, our main aim is to give the solution to two open problems which are posed by Bahramnezhad and Azar. Using this, we obtain that the space (L_{uo}(E,F)) of order bounded unbounded order continuous operators is an ideal in (L_{b}(E,F)) for Dedekind complete Riesz space F. In general, by giving an example that the space (L_{uo}(E,F)) of order bounded unbounded order continuous operators is not a band in ( L_{b}(E,F)), we obtain the conditions on E or F for the space ( L_{uo}(E,F)) to be a band in (L_{b}(E,F)). Then, we give the extension theorem for uo-continuous operators similar to Veksler’s theorem for order continuous operators.
{"title":"On unbounded order continuous operators 2","authors":"Bahri Turan, Hüma Gürkök","doi":"10.1007/s11117-023-01021-4","DOIUrl":"https://doi.org/10.1007/s11117-023-01021-4","url":null,"abstract":"<p>Let <i>E</i> and <i>F</i> be two Archimedean Riesz spaces. An operator <span>(T:Erightarrow F)</span> is said to be unbounded order continuous (<i>uo</i>-continuous), if <span>(u_{alpha }overset{uo}{rightarrow }0)</span> in <i>E</i> implies <span>(Tu_{alpha }overset{uo}{ rightarrow }0)</span> in <i>F</i>. In this study, our main aim is to give the solution to two open problems which are posed by Bahramnezhad and Azar. Using this, we obtain that the space <span>(L_{uo}(E,F))</span> of order bounded unbounded order continuous operators is an ideal in <span>(L_{b}(E,F))</span> for Dedekind complete Riesz space <i>F</i>. In general, by giving an example that the space <span>(L_{uo}(E,F))</span> of order bounded unbounded order continuous operators is not a band in <span>( L_{b}(E,F))</span>, we obtain the conditions on <i>E</i> or <i>F</i> for the space <span>( L_{uo}(E,F))</span> to be a band in <span>(L_{b}(E,F))</span>. Then, we give the extension theorem for <i>uo</i>-continuous operators similar to Veksler’s theorem for order continuous operators.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-26DOI: 10.1007/s11117-023-01022-3
J. C. Guella, J. Jäger
We present sufficient conditions for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their expansion in eigenfunctions of the Laplace–Beltrami operator. We also present a characterisation of this kernel class. The family analyzed is a generalization of the isotropic kernels and the case of a real sphere is analyzed in details.
{"title":"Strictly positive definite non-isotropic kernels on two-point homogeneous manifolds: the asymptotic approach","authors":"J. C. Guella, J. Jäger","doi":"10.1007/s11117-023-01022-3","DOIUrl":"https://doi.org/10.1007/s11117-023-01022-3","url":null,"abstract":"<p>We present sufficient conditions for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their expansion in eigenfunctions of the Laplace–Beltrami operator. We also present a characterisation of this kernel class. The family analyzed is a generalization of the isotropic kernels and the case of a real sphere is analyzed in details.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-09DOI: 10.1007/s11117-023-01019-y
Sameh Bououn
{"title":"The interplay between algebras and lattices: Stone–Weierstrass for illustration","authors":"Sameh Bououn","doi":"10.1007/s11117-023-01019-y","DOIUrl":"https://doi.org/10.1007/s11117-023-01019-y","url":null,"abstract":"","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135241757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-07DOI: 10.1007/s11117-023-01020-5
Raluca Dumitru, Jose A. Franco
{"title":"Near order and metric-like functions on the cone of positive definite matrices","authors":"Raluca Dumitru, Jose A. Franco","doi":"10.1007/s11117-023-01020-5","DOIUrl":"https://doi.org/10.1007/s11117-023-01020-5","url":null,"abstract":"","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-05DOI: 10.1007/s11117-023-01018-z
Sakshi Gupta, Rekha Gupta, Manjari Srivastava
{"title":"On scalarization and well-posedness in set optimization with a partial set order relation","authors":"Sakshi Gupta, Rekha Gupta, Manjari Srivastava","doi":"10.1007/s11117-023-01018-z","DOIUrl":"https://doi.org/10.1007/s11117-023-01018-z","url":null,"abstract":"","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135725041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-16DOI: 10.1007/s11117-023-01015-2
H. Raubenheimer, J. van Appel
Abstract Let A be a Banach algebra and let $$xin A$$ x∈A have the property that its spectrum does not separate 0 from infinity. It is well known that x has a logarithm, i.e., there exists $$yin A$$ y∈A with $$x=e^y$$ x=ey . We will use this statement to identify measures defined on a locally compact group to have logarithms. Also, we will show that the converse of the above statement is in general not true. Our results will be related to infinitely divisible probability measures.
摘要设A是一个Banach代数，且设$$xin A$$ x∈A具有其谱不将0与无穷分开的性质。众所周知，x有对数，即存在$$yin A$$ y∈a，且$$x=e^y$$ x = ey。我们将使用这个语句来确定在局部紧群上定义的具有对数的测度。同样，我们将证明上述陈述的反面通常是不正确的。我们的结果将与无限可分的概率测度有关。
{"title":"On logarithms of measures","authors":"H. Raubenheimer, J. van Appel","doi":"10.1007/s11117-023-01015-2","DOIUrl":"https://doi.org/10.1007/s11117-023-01015-2","url":null,"abstract":"Abstract Let A be a Banach algebra and let $$xin A$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> have the property that its spectrum does not separate 0 from infinity. It is well known that x has a logarithm, i.e., there exists $$yin A$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>y</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> with $$x=e^y$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>e</mml:mi> <mml:mi>y</mml:mi> </mml:msup> </mml:mrow> </mml:math> . We will use this statement to identify measures defined on a locally compact group to have logarithms. Also, we will show that the converse of the above statement is in general not true. Our results will be related to infinitely divisible probability measures.","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136078262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-15DOI: 10.1007/s11117-023-01016-1
Indranil Sarkar, Gaurav Singh
{"title":"On the uniqueness of continuous positive solution for a non-linear integral equation whose singularity lies in the reciprocal of the solution","authors":"Indranil Sarkar, Gaurav Singh","doi":"10.1007/s11117-023-01016-1","DOIUrl":"https://doi.org/10.1007/s11117-023-01016-1","url":null,"abstract":"","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136185844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-11DOI: 10.1007/s11117-023-01013-4
Evgeniya Burtseva, Lech Maligranda
Abstract We improve our results on boundedness of the Riesz potential in the central Morrey–Orlicz spaces and the corresponding weak-type version. We also present two new properties of the central Morrey–Orlicz spaces: nontriviality and inclusion property.
{"title":"A new result on boundedness of the Riesz potential in central Morrey–Orlicz spaces","authors":"Evgeniya Burtseva, Lech Maligranda","doi":"10.1007/s11117-023-01013-4","DOIUrl":"https://doi.org/10.1007/s11117-023-01013-4","url":null,"abstract":"Abstract We improve our results on boundedness of the Riesz potential in the central Morrey–Orlicz spaces and the corresponding weak-type version. We also present two new properties of the central Morrey–Orlicz spaces: nontriviality and inclusion property.","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136064067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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