{"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}
引用次数: 0
Abstract
A sufficient condition is established under which det(ABA−1B−1)=1\det (ABA^{-1}B^{-1})=1 for a pair of bounded, invertible operators A,BA,B on a Hilbert space.
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.