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Isomorphisms of spaces of affine continuous complex functions 仿射连续复函数空间的同构
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2019-10-19 DOI: 10.7146/math.scand.a-114989
Jakub Rondoš, J. Spurný
{"title":"Isomorphisms of spaces of affine continuous complex functions","authors":"Jakub Rondoš, J. Spurný","doi":"10.7146/math.scand.a-114989","DOIUrl":"https://doi.org/10.7146/math.scand.a-114989","url":null,"abstract":"Let $X$ and $Y$ be compact convex sets such that their each extreme point is a weak peak point. We show that $operatorname{ext} X$ is homeomorphic to $operatorname{ext} Y$ provided there exists a small-bound isomorphism of the space $mathfrak{A}(X,mathbb{C} )$ of continuous affine complex functions on $X$ onto $mathfrak{A}(Y,mathbb{C} )$. Further, we generalize a result of Cengiz to the context of compact convex sets.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41540628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Strong Morita equivalence for inclusions of $C^*$-algebras induced by twisted actions of a countable discrete group 由可数离散群的扭曲作用诱导的$C^*$-代数包含的强Morita等价
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2019-10-09 DOI: 10.7146/math.scand.a-125997
K. Kodaka
{"title":"Strong Morita equivalence for inclusions of $C^*$-algebras induced by twisted actions of a countable discrete group","authors":"K. Kodaka","doi":"10.7146/math.scand.a-125997","DOIUrl":"https://doi.org/10.7146/math.scand.a-125997","url":null,"abstract":"We consider two twisted actions of a countable discrete group on $sigma$-unital $C^*$-algebras. Then by taking the reduced crossed products, we get two inclusions of $C^*$-algebras. We suppose that they are strongly Morita equivalent as inclusions of $C^*$-algebras. Also, we suppose that one of the inclusions of $C^*$-algebras is irreducible, that is, the relative commutant of one of the $sigma$-unital $C^*$-algebra in the multiplier $C^*$-algebra of the reduced twisted crossed product is trivial. We show that the two actions are then strongly Morita equivalent up to some automorphism of the group.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46945713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Inhomogeneous Diophantine approximation over fields of formal power series 形式幂级数域上的非齐次丢番图近似
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2019-09-04 DOI: 10.7146/MATH.SCAND.A-121462
Y. Bugeaud, L. Singhal, Zhenliang Zhang
{"title":"Inhomogeneous Diophantine approximation over fields of formal power series","authors":"Y. Bugeaud, L. Singhal, Zhenliang Zhang","doi":"10.7146/MATH.SCAND.A-121462","DOIUrl":"https://doi.org/10.7146/MATH.SCAND.A-121462","url":null,"abstract":"We prove a sharp analogue of Minkowski's inhomogeneous approximation theorem over fields of power series Fq((T−1)). Furthermore, we study the approximation to a given point y– in Fq((T−1))2 by the SL2(Fq[T])-orbit of a given point x–– in Fq((T−1))2.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"126 1","pages":"451-478"},"PeriodicalIF":0.5,"publicationDate":"2019-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45853110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniqueness of norm-preserving extensions of functionals on the space of compact operators 紧致算子空间上泛函保模扩张的唯一性
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2019-08-29 DOI: 10.7146/math.scand.a-112071
Julia Martsinkevitš, M. Põldvere
{"title":"Uniqueness of norm-preserving extensions of functionals on the space of compact operators","authors":"Julia Martsinkevitš, M. Põldvere","doi":"10.7146/math.scand.a-112071","DOIUrl":"https://doi.org/10.7146/math.scand.a-112071","url":null,"abstract":"Godefroy, Kalton, and Saphar called a closed subspace $Y$ of a Banach space $Z$ an ideal if its annihilator $Y^bot $ is the kernel of a norm-one projection $P$ on the dual space $Z^ast $. If $Y$ is an ideal in $Z$ with respect to a projection on $Z^ast $ whose range is norming for $Z$, then $Y$ is said to be a strict ideal. We study uniqueness of norm-preserving extensions of functionals on the space $mathcal{K}(X,Y) $ of compact operators between Banach spaces $X$ and $Y$ to the larger space $mathcal{K}(X,Z) $ under the assumption that $Y$ is a strict ideal in $Z$. Our main results are: (1) if $y^ast $ is an extreme point of $B_{Y^{ast} }$ having a unique norm-preserving extension to $Z$, and $x^{astast} in B_{X^{astast} }$, then the only norm-preserving extension of the functional $x^{astast} otimes y^ast in mathcal {K}(X,Y)^ast $ to $mathcal {K}(X,Z)$ is $x^{astast} otimes z^ast $ where $z^ast in Z^ast $ is the only norm-preserving extension of $y^ast $ to $Z$; (2) if $mathcal{K}(X,Y) $ is an ideal in $mathcal{K}(X,Z) $ and $Y$ has Phelps' property $U$ in its bidual $Y^{astast} $ (i.e., every bounded linear functional on $Y$ admits a unique norm-preserving extension to $Y^{astast} $), then $mathcal{K}(X,Y) $ has property $U$ in $mathcal{K}(X,Z) $ whenever $X^{astast} $ has the Radon-Nikodým property.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43621043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi-symmetry without ratios 无比例的拟对称性
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2019-08-29 DOI: 10.7146/math.scand.a-112190
J. Kwapisz
{"title":"Quasi-symmetry without ratios","authors":"J. Kwapisz","doi":"10.7146/math.scand.a-112190","DOIUrl":"https://doi.org/10.7146/math.scand.a-112190","url":null,"abstract":"We characterize quasi-symmetric maps between compact metric spaces as homeomorphisms uniformly at all scales.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41487384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stable homotopy, $1$-dimensional NCCW complexes, and Property (H) 稳定同伦、$1$维NCCW配合物及其性质(H)
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2019-06-20 DOI: 10.7146/math.scand.a-121092
Qingnan An, G. Elliott, Zhichao Liu, Yuanhang Zhang
{"title":"Stable homotopy, $1$-dimensional NCCW complexes, and Property (H)","authors":"Qingnan An, G. Elliott, Zhichao Liu, Yuanhang Zhang","doi":"10.7146/math.scand.a-121092","DOIUrl":"https://doi.org/10.7146/math.scand.a-121092","url":null,"abstract":"In this paper, we show that the homomorphisms between two unital one-dimensional NCCW complexes with the same KK-class are stably homotopic, that is, after adding on a common homomorphism (with finite dimensional image), they are homotopic. As a consequence, any one-dimensional NCCW complex has the Property (H).","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42516451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A general one-sided compactness result for interpolation of bilinear operators 双线性算子插值的一般单侧紧性结果
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2019-06-17 DOI: 10.7146/MATH.SCAND.A-111424
E. B. D. Silva, D. L. Fernandez
{"title":"A general one-sided compactness result for interpolation of bilinear operators","authors":"E. B. D. Silva, D. L. Fernandez","doi":"10.7146/MATH.SCAND.A-111424","DOIUrl":"https://doi.org/10.7146/MATH.SCAND.A-111424","url":null,"abstract":"The behavior of bilinear operators acting on the interpolation of Banach spaces in relation to compactness is analyzed, and an one-sided compactness theorem is obtained for bilinear operators interpolated by the ρ interpolation method.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71059385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A family of reflexive vector bundles of reduction number one 一类归约数为1的自反向量丛
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2019-06-17 DOI: 10.7146/MATH.SCAND.A-111889
Cleto B. Miranda-Neto
{"title":"A family of reflexive vector bundles of reduction number one","authors":"Cleto B. Miranda-Neto","doi":"10.7146/MATH.SCAND.A-111889","DOIUrl":"https://doi.org/10.7146/MATH.SCAND.A-111889","url":null,"abstract":"A difficult issue in modern commutative algebra asks for examples of modules (more interestingly, reflexive vector bundles) having prescribed reduction number $rgeq 1$. The problem is even subtler if in addition we are interested in good properties for the Rees algebra. In this note we consider the case $r=1$. Precisely, we show that the module of logarithmic vector fields of the Fermat divisor of any degree in projective $3$-space is a reflexive vector bundle of reduction number $1$ and Gorenstein Rees ring.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48536467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The attainment set of the $varphi$-envelope and genericity properties $varphi$信封的实现集和泛型属性
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2019-06-17 DOI: 10.7146/MATH.SCAND.A-110766
A. Cabot, A. Jourani, L. Thibault, D. Zagrodny
{"title":"The attainment set of the $varphi$-envelope and genericity properties","authors":"A. Cabot, A. Jourani, L. Thibault, D. Zagrodny","doi":"10.7146/MATH.SCAND.A-110766","DOIUrl":"https://doi.org/10.7146/MATH.SCAND.A-110766","url":null,"abstract":"The attainment set of the $varphi$-envelope of a function at a given point is investigated. The inclusion of the attainment set of the $varphi$-envelope of the closed convex hull of a function into the attainment set of the function is preserved in sufficiently general settings to encompass the case $varphi$ being a norm in a power not less than $1$. The non-emptiness of the attainment set is guaranteed on generic subsets of a given space, in several fundamental cases.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49490852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Symmetric approximation sequences, Beilinson-Green algebras and derived equivalences 对称逼近序列、Beilinson-Green代数及其等价性
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2019-05-27 DOI: 10.7146/math.scand.a-133541
Shengyong Pan
{"title":"Symmetric approximation sequences, Beilinson-Green algebras and derived equivalences","authors":"Shengyong Pan","doi":"10.7146/math.scand.a-133541","DOIUrl":"https://doi.org/10.7146/math.scand.a-133541","url":null,"abstract":"In this paper, we will consider a class of locally $Phi$-Beilinson-Green algebras, where $Phi$ is an infinite admissible set of the integers, and show that symmetric approximation sequences in $n$-exangulated categories give rise to derived equivalences between quotient algebras of locally $Phi$-Beilinson-Green algebras in the principal diagonals modulo some factorizable ghost and coghost ideals by the locally finite tilting family. Then we get a class of derived equivalent algebras that have not been obtained by using previous techniques. From higher exact sequences, we obtain derived equivalences between subalgebras of endomorphism algebras by constructing tilting complexes, which generalizes Chen and Xi's result for exact sequences. From a given derived equivalence, we get derived equivalences between locally $Phi$-Beilinson-Green algebras of semi-Gorenstein modules. Finally, from given graded derived equivalences of group graded algebras, we get derived equivalences between associated Beilinson-Green algebras of group graded algebras.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47185906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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