Partial isometries and the conjecture of C.K. Fong and S.K. Tsui

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• 作者：Mostafa Mbekhta^a ; ^{mbekhta@math.univ-lille1.fr" class="auth_mail" title="E-mail the corresponding author} ; Laurian Suciu^b ; ^{laurians2002@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Partial isometry ; Quasi-isometry ; Nilpotent operator ; Brownian isometry
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：437
• 期：1
• 页码：431-444
• 全文大小：376 K

文摘

We investigate some bounded linear operators T   on a Hilbert space which satisfy the condition i1" class="mathmlsrc">i1.gif&_user=111111111&_pii=S0022247X15011907&_rdoc=1&_issn=0022247X&md5=6465e7780659d4520553826f515125aa" title="Click to view the MathML source">|T|≤|ReT|. We describe the maximum invariant subspace for a contraction T on which T is a partial isometry to obtain that, in certain cases, the above condition ensures that T is self-adjoint. In other words we show that the Fong–Tsui conjecture holds for partial isometries, contractive quasi-isometries, or 2-quasi-isometries, and Brownian isometries of positive covariance, or even for a more general class of operators.