Linear Algebra and its Applications, ( ISI ), Volume (591), Year (2020-4) , Pages (299-321)

Title : ( Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces )

Authors: Mohammad Sal Moslehian , Qingxiang Xu , ALi Zamani ,

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Abstract

Let A be a positive bounded operator on a Hilbert space . The semi-inner product , , induces a seminorm on . Let , and denote the A-operator seminorm, the A-numerical radius, and the A-Crawford number of an operator T in the semi-Hilbertian space , respectively. In this paper, we present some seminorm inequalities and equalities for semi-Hilbertian space operators. More precisely, we give some necessary and sufficient conditions for two orthogonal semi-Hilbertian operators satisfy Pythagoras\\\' equality. In addition, we derive new upper and lower bounds for the numerical radius of operators in semi-Hilbertian spaces. In particular, we show that where is the A-adjoint operator of T. Some applications of the newly obtained inequalities are also provided.

Keywords

, Positive operator Semi, inner product A, numerical radius Inequality
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@article{paperid:1078568,
author = {Sal Moslehian, Mohammad and Qingxiang Xu and علی زمانی},
title = {Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces},
journal = {Linear Algebra and its Applications},
year = {2020},
volume = {591},
month = {April},
issn = {0024-3795},
pages = {299--321},
numpages = {22},
keywords = {Positive operator Semi-inner product A-numerical radius Inequality},
}

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%0 Journal Article
%T Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces
%A Sal Moslehian, Mohammad
%A Qingxiang Xu
%A علی زمانی
%J Linear Algebra and its Applications
%@ 0024-3795
%D 2020

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