Pub Date : 2019-10-19DOI: 10.7146/math.scand.a-114989
Jakub Rondoš, J. Spurný
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.
{"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}
Pub Date : 2019-10-09DOI: 10.7146/math.scand.a-125997
K. Kodaka
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.
{"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}
Pub Date : 2019-09-04DOI: 10.7146/MATH.SCAND.A-121462
Y. Bugeaud, L. Singhal, Zhenliang Zhang
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.
{"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}
Pub Date : 2019-08-29DOI: 10.7146/math.scand.a-112071
Julia Martsinkevitš, M. Põldvere
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.
{"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}
Pub Date : 2019-08-29DOI: 10.7146/math.scand.a-112190
J. Kwapisz
We characterize quasi-symmetric maps between compact metric spaces as homeomorphisms uniformly at all scales.
我们将紧致度量空间之间的拟对称映射刻画为在所有尺度上一致的同胚。
{"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}
Pub Date : 2019-06-20DOI: 10.7146/math.scand.a-121092
Qingnan An, G. Elliott, Zhichao Liu, Yuanhang Zhang
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).
{"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}
Pub Date : 2019-06-17DOI: 10.7146/MATH.SCAND.A-111424
E. B. D. Silva, D. L. Fernandez
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.
{"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}
Pub Date : 2019-06-17DOI: 10.7146/MATH.SCAND.A-111889
Cleto B. Miranda-Neto
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.
{"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}
Pub Date : 2019-06-17DOI: 10.7146/MATH.SCAND.A-110766
A. Cabot, A. Jourani, L. Thibault, D. Zagrodny
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.
{"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}
Pub Date : 2019-05-27DOI: 10.7146/math.scand.a-133541
Shengyong Pan
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.
{"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}
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