چهل و یکمین کنفرانس ریاضی کشور , 2010-09-12

Title : ( On Fuglede--Putnam type theorems )

Authors: Mohammad Sal Moslehian , sadegh nabavi ,

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Abstract

Let $A, B, X \\in \\mathbb{B}(\\mathcal{H})$ for some complex Hilbert space $\\mathcal{H}$ and $\\tilde{A}$ denote the Aluthge transformation of $A$. Then $AX=XB$ implies $\\tilde{A}X=X\\tilde{B}$, whenever it implies that $A^* X=XB^*$. We show that if $A ,B^*$ are log-hyponormal and $\\tilde{A}X=X\\tilde{B}$ then $AX=XB$. If $A=U|A|$ be the polar decomposition of $A$, $U|A|^{1\\over2}\\geq a\\geq0$ and $X$ is an operator such that $U^* X=XU$, then we prove that $\\|\\tilde{A}^* X-X\\tilde{A}\\|_p\\geq 2a\\||A|^{1\\over2}X-X|A|^{1\\over2}\\|_p$.

Keywords

, Fuglede, , Putnam theorem; Aluthge transformation; norm inequality; hyponormal; log, hyponormal; $p$, hyponormal; polar decomposition; Schatten $p$, norm
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@inproceedings{paperid:1020955,
author = {Sal Moslehian, Mohammad and Nabavi, Sadegh},
title = {On Fuglede--Putnam type theorems},
booktitle = {چهل و یکمین کنفرانس ریاضی کشور},
year = {2010},
location = {ارومیه, IRAN},
keywords = {Fuglede--Putnam theorem; Aluthge transformation; norm inequality; hyponormal; log-hyponormal; $p$-hyponormal; polar decomposition; Schatten $p$-norm},
}

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%0 Conference Proceedings
%T On Fuglede--Putnam type theorems
%A Sal Moslehian, Mohammad
%A Nabavi, Sadegh
%J چهل و یکمین کنفرانس ریاضی کشور
%D 2010

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