Bulletin of the Australian Mathematical Society最新文献

{"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}

{"title":"ANY DUAL OPERATOR SPACE IS WEAKLY LOCALLY REFLEXIVE","authors":"ZHE DONG, JINZE JIANG, YAFEI ZHAO","doi":"10.1017/s0004972723001120","DOIUrl":"https://doi.org/10.1017/s0004972723001120","url":null,"abstract":"<p>We introduce the notion of weakly local reflexivity in operator space theory and prove that any dual operator space is weakly locally reflexive.</p>","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"10 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138575739","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}

{"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}

{"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}

{"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 &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline1.png\" /&gt; &lt;jats:tex-math&gt; $K={mathbb {Q}}(theta )$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; be an algebraic number field with &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline2.png\" /&gt; &lt;jats:tex-math&gt; $theta $ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; satisfying a monic irreducible polynomial &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline3.png\" /&gt; &lt;jats:tex-math&gt; $f(x)$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; of degree &lt;jats:italic&gt;n&lt;/jats:italic&gt; over &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline4.png\" /&gt; &lt;jats:tex-math&gt; ${mathbb {Q}}.$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; The polynomial &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline5.png\" /&gt; &lt;jats:tex-math&gt; $f(x)$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; is said to be monogenic if &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline6.png\" /&gt; &lt;jats:tex-math&gt; ${1,theta ,ldots ,theta ^{n-1}}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; is an integral basis of &lt;jats:italic&gt;K&lt;/jats:italic&gt;. 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’, &lt;jats:italic&gt;Bull. Aust. Math. Soc.&lt;/jats:italic&gt;100 (2019), 239–244] conjectured that if &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline7.png\" /&gt; &lt;jats:tex-math&gt; $nge 3$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline8.png\" /&gt; &lt;jats:tex-math&gt; $1le mle n-1$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001119_inline9.png\" /&gt; &lt;jats:tex-math&gt; $gcd (n,mB)=1$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; and &lt;jats:italic&gt;A&lt;/jats:italic&gt; 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}

{"title":"ADDITIVE COMPLETION OF THIN SETS","authors":"JIN-HUI FANG, CSABA SÁNDOR","doi":"10.1017/s0004972723001016","DOIUrl":"https://doi.org/10.1017/s0004972723001016","url":null,"abstract":"Two sets &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline1.png\" /&gt; &lt;jats:tex-math&gt; $A,B$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; of positive integers are called &lt;jats:italic&gt;exact additive complements&lt;/jats:italic&gt; if &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline2.png\" /&gt; &lt;jats:tex-math&gt; $A+B$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; contains all sufficiently large integers and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline3.png\" /&gt; &lt;jats:tex-math&gt; $A(x)B(x)/xrightarrow 1$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;. For &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline4.png\" /&gt; &lt;jats:tex-math&gt; $A={a_1&lt;a_2&lt;cdots }$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, let &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline5.png\" /&gt; &lt;jats:tex-math&gt; $A(x)$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; denote the counting function of &lt;jats:italic&gt;A&lt;/jats:italic&gt; and let &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline6.png\" /&gt; &lt;jats:tex-math&gt; $a^*(x)$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; denote the largest element in &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline7.png\" /&gt; &lt;jats:tex-math&gt; $Abigcap [1,x]$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;. Following the work of Ruzsa [‘Exact additive complements’, &lt;jats:italic&gt;Quart. J. Math.&lt;/jats:italic&gt;68 (2017) 227–235] and Chen and Fang [‘Additive complements with Narkiewicz’s condition’, &lt;jats:italic&gt;Combinatorica&lt;/jats:italic&gt;39 (2019), 813–823], we prove that, for exact additive complements &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline8.png\" /&gt; &lt;jats:tex-math&gt; $A,B$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; with &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline9.png\" /&gt; &lt;jats:tex-math&gt; ${a_{n+1}}/ {na_n}rightarrow infty $ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, &lt;jats:disp-formula&gt; &lt;jats:alternatives&gt; &lt;jats:graphic xmlns:xlink=\"http:","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"220 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495304","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}

{"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}

{"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}

{"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}

{"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}