Comptes Rendus Mathematique , ( ISI ), Volume (350), No (2), Year (2012-6) , Pages (407-410)

Title : ( On the binary relation leq_u on self-adjoint Hilbert space operators )

Authors: Mohammad Sal Moslehian , sadegh nabavi , Hamed Najafi ,

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Abstract

Given self-adjoint operators A, B in mathbb{B}( mathscr{H}) it is said A leq_uB whenever A leq U^*BU for some unitary operator U . We show that A leq_u B if and only if f(g(A)^r) leq_uf(g(B)^r) for any increasing operator convex function f , any operator monotone function g and any positive number r . We present some sufficient conditions under which if B leq A leq U^*BU$, then B=A=U^*BU . Finally we prove that if A^n leq U^ ast A^nU$ for all n in mathbb{N} , then A=U^ ast AU .

Keywords

Operator inequality; binary order; operator convex function; hyponormal; strong operator topology
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@article{paperid:1028014,
author = {Sal Moslehian, Mohammad and Nabavi, Sadegh and Najafi, Hamed},
title = {On the binary relation leq_u on self-adjoint Hilbert space operators},
journal = {Comptes Rendus Mathematique },
year = {2012},
volume = {350},
number = {2},
month = {June},
issn = {1631-073X},
pages = {407--410},
numpages = {3},
keywords = {Operator inequality; binary order; operator convex function; hyponormal; strong operator topology},
}

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%0 Journal Article
%T On the binary relation leq_u on self-adjoint Hilbert space operators
%A Sal Moslehian, Mohammad
%A Nabavi, Sadegh
%A Najafi, Hamed
%J Comptes Rendus Mathematique
%@ 1631-073X
%D 2012

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