Pub Date : 2023-09-01DOI: 10.4153/s0008439523000644
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
{"title":"BCM volume 66 issue 3 Cover and Back matter","authors":"","doi":"10.4153/s0008439523000644","DOIUrl":"https://doi.org/10.4153/s0008439523000644","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135304842","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 : 2023-08-14DOI: 10.4153/s0008439523000619
Qianshun Cui, Zejun Hu
{"title":"Nonexistence of non-Hopf Ricci-semisymmetric real hypersurfaces in and","authors":"Qianshun Cui, Zejun Hu","doi":"10.4153/s0008439523000619","DOIUrl":"https://doi.org/10.4153/s0008439523000619","url":null,"abstract":"","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44408928","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 : 2023-07-10DOI: 10.4153/s0008439523000589
H. Kaptanoğlu
{"title":"UNCERTAINTY PRINCIPLES IN HOLOMORPHIC FUNCTION SPACES ON THE UNIT BALL","authors":"H. Kaptanoğlu","doi":"10.4153/s0008439523000589","DOIUrl":"https://doi.org/10.4153/s0008439523000589","url":null,"abstract":"","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45339925","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 : 2023-07-03DOI: 10.4153/S0008439523000620
G. Babu, H. K. Mishra
Williamson's theorem states that for any $2n times 2n$ real positive definite matrix $A$, there exists a $2n times 2n$ real symplectic matrix $S$ such that $S^TAS=D oplus D$, where $D$ is an $ntimes n$ diagonal matrix with positive diagonal entries which are known as the symplectic eigenvalues of $A$. Let $H$ be any $2n times 2n$ real symmetric matrix such that the perturbed matrix $A+H$ is also positive definite. In this paper, we show that any symplectic matrix $tilde{S}$ diagonalizing $A+H$ in Williamson's theorem is of the form $tilde{S}=S Q+mathcal{O}(|H|)$, where $Q$ is a $2n times 2n$ real symplectic as well as orthogonal matrix. Moreover, $Q$ is in $textit{symplectic block diagonal}$ form with the block sizes given by twice the multiplicities of the symplectic eigenvalues of $A$. Consequently, we show that $tilde{S}$ and $S$ can be chosen so that $|tilde{S}-S|=mathcal{O}(|H|)$. Our results hold even if $A$ has repeated symplectic eigenvalues. This generalizes the stability result of symplectic matrices for non-repeated symplectic eigenvalues given by Idel, Gaona, and Wolf [$textit{Linear Algebra Appl., 525:45-58, 2017}$].
Williamson定理指出，对于任何$2n times 2n$实正定矩阵$A$，存在一个$2n times 2n$实辛矩阵$S$，使得$S^TAS=D oplus D$，其中$D$是一个$ntimes n$对角矩阵，其对角项被称为$A$的辛特征值。设$H$为任意$2n times 2n$实对称矩阵，使得扰动矩阵$A+H$也是正定的。本文证明了Williamson定理中对角化$A+H$的任何辛矩阵$tilde{S}$的形式为$tilde{S}=S Q+mathcal{O}(|H|)$，其中$Q$是一个$2n times 2n$实辛矩阵和正交矩阵。此外，$Q$是$textit{symplectic block diagonal}$形式，其块大小由$A$的辛特征值的两倍多重给出。因此，我们表明可以选择$tilde{S}$和$S$，以便$|tilde{S}-S|=mathcal{O}(|H|)$。即使$A$有重复的辛特征值，我们的结果也成立。这推广了Idel, Gaona, and Wolf [$textit{Linear Algebra Appl., 525:45-58, 2017}$]给出的辛矩阵对于非重复辛特征值的稳定性结果。
{"title":"Block perturbation of symplectic matrices in Williamson’s theorem","authors":"G. Babu, H. K. Mishra","doi":"10.4153/S0008439523000620","DOIUrl":"https://doi.org/10.4153/S0008439523000620","url":null,"abstract":"Williamson's theorem states that for any $2n times 2n$ real positive definite matrix $A$, there exists a $2n times 2n$ real symplectic matrix $S$ such that $S^TAS=D oplus D$, where $D$ is an $ntimes n$ diagonal matrix with positive diagonal entries which are known as the symplectic eigenvalues of $A$. Let $H$ be any $2n times 2n$ real symmetric matrix such that the perturbed matrix $A+H$ is also positive definite. In this paper, we show that any symplectic matrix $tilde{S}$ diagonalizing $A+H$ in Williamson's theorem is of the form $tilde{S}=S Q+mathcal{O}(|H|)$, where $Q$ is a $2n times 2n$ real symplectic as well as orthogonal matrix. Moreover, $Q$ is in $textit{symplectic block diagonal}$ form with the block sizes given by twice the multiplicities of the symplectic eigenvalues of $A$. Consequently, we show that $tilde{S}$ and $S$ can be chosen so that $|tilde{S}-S|=mathcal{O}(|H|)$. Our results hold even if $A$ has repeated symplectic eigenvalues. This generalizes the stability result of symplectic matrices for non-repeated symplectic eigenvalues given by Idel, Gaona, and Wolf [$textit{Linear Algebra Appl., 525:45-58, 2017}$].","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48951194","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 : 2023-06-27DOI: 10.4153/s0008439523000553
Nilanjan Das
The purpose of this note is to obtain an improved lower bound for the multidimensional Bohr radius introduced by L. Aizenberg (2000, Proceedings of the American Mathematical Society 128, 1147–1155), by means of a rather simple argument.
{"title":"A logarithmic lower bound for the second Bohr radius","authors":"Nilanjan Das","doi":"10.4153/s0008439523000553","DOIUrl":"https://doi.org/10.4153/s0008439523000553","url":null,"abstract":"\u0000 The purpose of this note is to obtain an improved lower bound for the multidimensional Bohr radius introduced by L. Aizenberg (2000, Proceedings of the American Mathematical Society 128, 1147–1155), by means of a rather simple argument.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44397314","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 : 2023-06-13DOI: 10.4153/s0008439523000498
F. Hajir, Christian Maire, Ravi Ramakrishna
The tame Gras–Munnier Theorem gives a criterion for the existence of a $ {mathbb Z}/p{mathbb Z} $ -extension of a number field K ramified at exactly a tame set S of places of K, the finite $v in S$ necessarily having norm $1$ mod p. The criterion is the existence of a nontrivial dependence relation on the Frobenius elements of these places in a certain governing extension. We give a short new proof which extends the theorem by showing the subset of elements of $H^1(G_S,{mathbb {Z}}/p{mathbb {Z}})$ giving rise to such extensions of K has the same cardinality as the set of these dependence relations. We then reprove the key Proposition 2.2 using the more sophisticated Greenberg–Wiles formula based on global duality.
{"title":"On tame -extensions with prescribed ramification","authors":"F. Hajir, Christian Maire, Ravi Ramakrishna","doi":"10.4153/s0008439523000498","DOIUrl":"https://doi.org/10.4153/s0008439523000498","url":null,"abstract":"\u0000 The tame Gras–Munnier Theorem gives a criterion for the existence of a \u0000 \u0000 \u0000 \u0000$ {mathbb Z}/p{mathbb Z} $\u0000\u0000 \u0000 -extension of a number field K ramified at exactly a tame set S of places of K, the finite \u0000 \u0000 \u0000 \u0000$v in S$\u0000\u0000 \u0000 necessarily having norm \u0000 \u0000 \u0000 \u0000$1$\u0000\u0000 \u0000 mod p. The criterion is the existence of a nontrivial dependence relation on the Frobenius elements of these places in a certain governing extension. We give a short new proof which extends the theorem by showing the subset of elements of \u0000 \u0000 \u0000 \u0000$H^1(G_S,{mathbb {Z}}/p{mathbb {Z}})$\u0000\u0000 \u0000 giving rise to such extensions of K has the same cardinality as the set of these dependence relations. We then reprove the key Proposition 2.2 using the more sophisticated Greenberg–Wiles formula based on global duality.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47743147","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 : 2023-06-09DOI: 10.4153/s0008439523000474
S. Ahammed, M. B. Ahamed
In this article, we prove several refined versions of the classical Bohr inequality for the class of analytic self-mappings on the unit disk $ mathbb {D} $ , class of analytic functions $ f $ defined on $ mathbb {D} $ such that $mathrm {Re}left (f(z)right )<1 $ , and class of subordination to a function g in $ mathbb {D} $ . Consequently, the main results of this article are established as certainly improved versions of several existing results. All the results are proved to be sharp.
{"title":"Refined Bohr inequalities for certain classes of functions: analytic, univalent, and convex","authors":"S. Ahammed, M. B. Ahamed","doi":"10.4153/s0008439523000474","DOIUrl":"https://doi.org/10.4153/s0008439523000474","url":null,"abstract":"\u0000\t <jats:p>In this article, we prove several refined versions of the classical Bohr inequality for the class of analytic self-mappings on the unit disk <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0008439523000474_inline1.png\" />\u0000\t\t<jats:tex-math>\u0000$ mathbb {D} $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>, class of analytic functions <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0008439523000474_inline2.png\" />\u0000\t\t<jats:tex-math>\u0000$ f $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> defined on <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0008439523000474_inline3.png\" />\u0000\t\t<jats:tex-math>\u0000$ mathbb {D} $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> such that <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0008439523000474_inline4.png\" />\u0000\t\t<jats:tex-math>\u0000$mathrm {Re}left (f(z)right )<1 $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>, and class of subordination to a function <jats:italic>g</jats:italic> in <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0008439523000474_inline5.png\" />\u0000\t\t<jats:tex-math>\u0000$ mathbb {D} $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>. Consequently, the main results of this article are established as certainly improved versions of several existing results. All the results are proved to be sharp.</jats:p>","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44191180","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 : 2023-06-07DOI: 10.4153/s0008439523000462
Jaewoong Kim, Jasang Yoon
In this paper, we introduce the spherical polar decomposition of the linear pencil of an ordered pair $mathbf {T}=(T_{1},T_{2})$ and investigate nontrivial invariant subspaces between the generalized spherical Aluthge transform of the linear pencil of $mathbf {T}$ and the linear pencil of the original pair $mathbf {T}$ of bounded operators with dense ranges.
{"title":"Nontrivial invariant subspaces of linear operator pencils","authors":"Jaewoong Kim, Jasang Yoon","doi":"10.4153/s0008439523000462","DOIUrl":"https://doi.org/10.4153/s0008439523000462","url":null,"abstract":"\u0000 In this paper, we introduce the spherical polar decomposition of the linear pencil of an ordered pair \u0000 \u0000 \u0000 \u0000$mathbf {T}=(T_{1},T_{2})$\u0000\u0000 \u0000 and investigate nontrivial invariant subspaces between the generalized spherical Aluthge transform of the linear pencil of \u0000 \u0000 \u0000 \u0000$mathbf {T}$\u0000\u0000 \u0000 and the linear pencil of the original pair \u0000 \u0000 \u0000 \u0000$mathbf {T}$\u0000\u0000 \u0000 of bounded operators with dense ranges.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42406214","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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