关于基塔耶夫行列式

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2024-04-12 DOI:10.1090/spmj/1796

A. Elgart, M. Fraas

{"title":"关于基塔耶夫行列式","authors":"A. Elgart, M. Fraas","doi":"10.1090/spmj/1796","DOIUrl":null,"url":null,"abstract":"<p>A sufficient condition is established under which <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"det left-parenthesis upper A upper B upper A Superscript negative 1 Baseline upper B Superscript negative 1 Baseline right-parenthesis equals 1\"> <mml:semantics> <mml:mrow> <mml:mo movablelimits=\"true\" form=\"prefix\">det</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>A</mml:mi> <mml:mi>B</mml:mi> <mml:msup> <mml:mi>A</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mi>B</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">\\det (ABA^{-1}B^{-1})=1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for a pair of bounded, invertible operators <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A comma upper B\"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>,</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">A,B</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on a Hilbert space.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":"162 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Kitaev’s determinant formula\",\"authors\":\"A. Elgart, M. Fraas\",\"doi\":\"10.1090/spmj/1796\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A sufficient condition is established under which <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"det left-parenthesis upper A upper B upper A Superscript negative 1 Baseline upper B Superscript negative 1 Baseline right-parenthesis equals 1\\\"> <mml:semantics> <mml:mrow> <mml:mo movablelimits=\\\"true\\\" form=\\\"prefix\\\">det</mml:mo> <mml:mo stretchy=\\\"false\\\">(</mml:mo> <mml:mi>A</mml:mi> <mml:mi>B</mml:mi> <mml:msup> <mml:mi>A</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mi>B</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy=\\\"false\\\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">\\\\det (ABA^{-1}B^{-1})=1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for a pair of bounded, invertible operators <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper A comma upper B\\\"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>,</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">A,B</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on a Hilbert space.</p>\",\"PeriodicalId\":51162,\"journal\":{\"name\":\"St Petersburg Mathematical Journal\",\"volume\":\"162 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"St Petersburg Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/spmj/1796\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1796","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

对于希尔伯特空间上的一对有界可逆算子 A , B A,B 来说，det ( A B A - 1 B - 1 ) = 1 \det (ABA^{-1}B^{-1})=1 是一个充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On Kitaev’s determinant formula

A sufficient condition is established under which det ( A B A − 1 B − 1 ) = 1 \det (ABA^{-1}B^{-1})=1 for a pair of bounded, invertible operators A , B A,B on a Hilbert space.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.