Pub Date : 2023-12-18DOI: 10.1017/s000497272300117x
BO YU, JIANKUI LI
Let H be a complex separable Hilbert space with $dim H geq 2$. Let $mathcal {N}$ be a nest on H such that $E_+ neq E$ for any $E neq H, E in mathcal {N}$. We prove that every 2-local isometry of $operatorname {Alg}mathcal {N}$ is a surjective linear isometry.
让 H 是一个复杂的可分离的希尔伯特空间，其中有 $dim H geq 2$。让 $mathcal {N}$ 是 H 上的一个巢，对于任意 $E neq H, E in mathcal {N}$ 来说，$E_+ neq E$ 是这样的。我们证明 $operatorname {Alg}mathcal {N}$ 的每一个 2 局部等势都是投射线性等势。
{"title":"2-LOCAL ISOMETRIES OF SOME NEST ALGEBRAS","authors":"BO YU, JIANKUI LI","doi":"10.1017/s000497272300117x","DOIUrl":"https://doi.org/10.1017/s000497272300117x","url":null,"abstract":"<p>Let <span>H</span> be a complex separable Hilbert space with <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231216090148228-0567:S000497272300117X:S000497272300117X_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$dim H geq 2$</span></span></img></span></span>. Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231216090148228-0567:S000497272300117X:S000497272300117X_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal {N}$</span></span></img></span></span> be a nest on <span>H</span> such that <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231216090148228-0567:S000497272300117X:S000497272300117X_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$E_+ neq E$</span></span></img></span></span> for any <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231216090148228-0567:S000497272300117X:S000497272300117X_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$E neq H, E in mathcal {N}$</span></span></img></span></span>. We prove that every 2-local isometry of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231216090148228-0567:S000497272300117X:S000497272300117X_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$operatorname {Alg}mathcal {N}$</span></span></img></span></span> is a surjective linear isometry.</p>","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138714876","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 : 2023-12-12DOI: 10.1017/s0004972723001120
ZHE DONG, JINZE JIANG, YAFEI ZHAO
We introduce the notion of weakly local reflexivity in operator space theory and prove that any dual operator space is weakly locally reflexive.
我们在算子空间理论中引入了弱局部反折的概念，并证明任何对偶算子空间都是弱局部反折的。
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Pub Date : 2023-12-12DOI: 10.1017/s0004972723001144
Behrooz Niknami
{"title":"Stochastic Matching Models","authors":"Behrooz Niknami","doi":"10.1017/s0004972723001144","DOIUrl":"https://doi.org/10.1017/s0004972723001144","url":null,"abstract":"","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"48 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139009806","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 : 2023-12-12DOI: 10.1017/s0004972723001132
A. Simonič
{"title":"NEW EFFECTIVE RESULTS IN THE THEORY OF THE RIEMANN ZETA-FUNCTION","authors":"A. Simonič","doi":"10.1017/s0004972723001132","DOIUrl":"https://doi.org/10.1017/s0004972723001132","url":null,"abstract":"","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"19 25","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138977190","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 : 2023-11-21DOI: 10.1017/s0004972723001119
SUMANDEEP KAUR, SURENDER KUMAR
Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0004972723001119_inline1.png" /> <jats:tex-math> $K={mathbb {Q}}(theta )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be an algebraic number field with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0004972723001119_inline2.png" /> <jats:tex-math> $theta $ </jats:tex-math> </jats:alternatives> </jats:inline-formula> satisfying a monic irreducible polynomial <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0004972723001119_inline3.png" /> <jats:tex-math> $f(x)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> of degree <jats:italic>n</jats:italic> over <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0004972723001119_inline4.png" /> <jats:tex-math> ${mathbb {Q}}.$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> The polynomial <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0004972723001119_inline5.png" /> <jats:tex-math> $f(x)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is said to be monogenic if <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0004972723001119_inline6.png" /> <jats:tex-math> ${1,theta ,ldots ,theta ^{n-1}}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is an integral basis of <jats:italic>K</jats:italic>. Deciding whether or not a monic irreducible polynomial is monogenic is an important problem in algebraic number theory. In an attempt to answer this problem for a certain family of polynomials, Jones [‘A brief note on some infinite families of monogenic polynomials’, <jats:italic>Bull. Aust. Math. Soc.</jats:italic>100 (2019), 239–244] conjectured that if <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0004972723001119_inline7.png" /> <jats:tex-math> $nge 3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0004972723001119_inline8.png" /> <jats:tex-math> $1le mle n-1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0004972723001119_inline9.png" /> <jats:tex-math> $gcd (n,mB)=1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:italic>A</jats:italic> is a prime number, th
{"title":"ON A CONJECTURE OF LENNY JONES ABOUT CERTAIN MONOGENIC POLYNOMIALS","authors":"SUMANDEEP KAUR, SURENDER KUMAR","doi":"10.1017/s0004972723001119","DOIUrl":"https://doi.org/10.1017/s0004972723001119","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline1.png\" /> <jats:tex-math> $K={mathbb {Q}}(theta )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be an algebraic number field with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline2.png\" /> <jats:tex-math> $theta $ </jats:tex-math> </jats:alternatives> </jats:inline-formula> satisfying a monic irreducible polynomial <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline3.png\" /> <jats:tex-math> $f(x)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> of degree <jats:italic>n</jats:italic> over <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline4.png\" /> <jats:tex-math> ${mathbb {Q}}.$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> The polynomial <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline5.png\" /> <jats:tex-math> $f(x)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is said to be monogenic if <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline6.png\" /> <jats:tex-math> ${1,theta ,ldots ,theta ^{n-1}}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is an integral basis of <jats:italic>K</jats:italic>. Deciding whether or not a monic irreducible polynomial is monogenic is an important problem in algebraic number theory. In an attempt to answer this problem for a certain family of polynomials, Jones [‘A brief note on some infinite families of monogenic polynomials’, <jats:italic>Bull. Aust. Math. Soc.</jats:italic>100 (2019), 239–244] conjectured that if <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline7.png\" /> <jats:tex-math> $nge 3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline8.png\" /> <jats:tex-math> $1le mle n-1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline9.png\" /> <jats:tex-math> $gcd (n,mB)=1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:italic>A</jats:italic> is a prime number, th","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"220 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495303","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 : 2023-11-08DOI: 10.1017/s0004972722001538
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{"title":"AUTHOR INDEX FOR VOLUME 108","authors":"","doi":"10.1017/s0004972722001538","DOIUrl":"https://doi.org/10.1017/s0004972722001538","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"31 S105","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343221","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 : 2023-11-08DOI: 10.1017/s0004972722001526
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":"BAZ volume 108 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s0004972722001526","DOIUrl":"https://doi.org/10.1017/s0004972722001526","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":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"30 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343235","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 : 2023-11-08DOI: 10.1017/s0004972722001514
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":"BAZ volume 108 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s0004972722001514","DOIUrl":"https://doi.org/10.1017/s0004972722001514","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":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"29 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343047","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 : 2023-11-07DOI: 10.1017/s0004972723001090
PAYMAN ESKANDARI
Abstract We prove analogues of Schur’s lemma for endomorphisms of extensions in Tannakian categories. More precisely, let $mathbf {T}$ be a neutral Tannakian category over a field of characteristic zero. Let E be an extension of A by B in $mathbf {T}$ . We consider conditions under which every endomorphism of E that stabilises B induces a scalar map on $Aoplus B$ . We give a result in this direction in the general setting of arbitrary $mathbf {T}$ and E , and then a stronger result when $mathbf {T}$ is filtered and the associated graded objects to A and B satisfy some conditions. We also discuss the sharpness of the results.
摘要证明了Tannakian范畴中扩展自同态的Schur引理的类似物。更准确地说，设$mathbf {T}$是特征为零的域上的中性Tannakian范畴。设E是$mathbf {T}$中A乘以B的扩展。我们考虑了稳定B的E的每一个自同态在$ a 0 + $ B上诱导一个标量映射的条件。我们在任意$mathbf {T}$和E的一般设置下给出了这个方向的结果，然后在$mathbf {T}$被过滤并且关联到a和B的分级对象满足某些条件时给出了一个更强的结果。我们还讨论了结果的清晰度。
{"title":"ON ENDOMORPHISMS OF EXTENSIONS IN TANNAKIAN CATEGORIES","authors":"PAYMAN ESKANDARI","doi":"10.1017/s0004972723001090","DOIUrl":"https://doi.org/10.1017/s0004972723001090","url":null,"abstract":"Abstract We prove analogues of Schur’s lemma for endomorphisms of extensions in Tannakian categories. More precisely, let $mathbf {T}$ be a neutral Tannakian category over a field of characteristic zero. Let E be an extension of A by B in $mathbf {T}$ . We consider conditions under which every endomorphism of E that stabilises B induces a scalar map on $Aoplus B$ . We give a result in this direction in the general setting of arbitrary $mathbf {T}$ and E , and then a stronger result when $mathbf {T}$ is filtered and the associated graded objects to A and B satisfy some conditions. We also discuss the sharpness of the results.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"12 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135480126","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}
$dim H geq 2$. Let 
$mathcal {N}$ be a nest on H such that 
$E_+ neq E$ for any 
$E neq H, E in mathcal {N}$. We prove that every 2-local isometry of 
$operatorname {Alg}mathcal {N}$ is a surjective linear isometry.
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