Bulletin of the Malaysian Mathematical Sciences Society, ( ISI ), Volume (42), No (5), Year (2019-9) , Pages (2135-2149)

Title : ( An Operator Inequality for Bounded Linear Maps Between $$C^*$$ C ∗ -Algebras )

Authors: Mohammad Sal Moslehian , Hamed Najafi , Mohsen Kian ,

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Abstract

‎In this paper‎, ‎we prove that if Phi‎: mathscr{A} to mathscr{B} is a bounded linear map between C^*-algebras‎, ‎then‎ begin{equation*}‎ left|sum_{k=1}^n left{|Phi(A_k)|^2+|Phi(A_k^*)|^2right}right|leq 2 |Phi|^2 left | sum_{k=1}^n‎ ‎ left( |A_k|^2+|A_k^*|^2 right) right |‎ ‎ end{equation*}‎ ‎for all $n in mathbb{N}$ and all $A_1, ldots‎, ‎A_n in mathscr{A}$‎. ‎This improves the Haagerup--Pisier--Ringrose (H-P-R) inequality for Hermitian bounded maps Phi‎. ‎In addition‎, ‎we present a refinement of the H-P-R inequality and give an example to support it‎. ‎Moreover‎, ‎we establish several versions of the H-P-R inequality involving unitarily invariant norms‎. ‎Further‎, ‎we present some useful inequalities in the setting of Hilbert C^*-modules and then apply it to get several H-P-R type inequalities‎.

Keywords

, Haagerup--Pisier--Ringrose inequality; positive map; C^*-algebra; unitarily invariant norm, test
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@article{paperid:1074684,
author = {Sal Moslehian, Mohammad and Najafi, Hamed and Mohsen Kian},
title = {An Operator Inequality for Bounded Linear Maps Between $$C^*$$ C ∗ -Algebras},
journal = {Bulletin of the Malaysian Mathematical Sciences Society},
year = {2019},
volume = {42},
number = {5},
month = {September},
issn = {0126-6705},
pages = {2135--2149},
numpages = {14},
keywords = {Haagerup--Pisier--Ringrose inequality; positive map; C^*-algebra; unitarily invariant norm;test},
}

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%0 Journal Article
%T An Operator Inequality for Bounded Linear Maps Between $$C^*$$ C ∗ -Algebras
%A Sal Moslehian, Mohammad
%A Najafi, Hamed
%A Mohsen Kian
%J Bulletin of the Malaysian Mathematical Sciences Society
%@ 0126-6705
%D 2019

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