Title : ( An Operator Inequality for Bounded Linear Maps Between $$C^*$$-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
@article{paperid:1074684,
author = {Sal Moslehian, Mohammad and Najafi, Hamed and Mohsen Kian},
title = {An Operator Inequality for Bounded Linear Maps Between $$C^*$$-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},
}
%0 Journal Article
%T An Operator Inequality for Bounded Linear Maps Between $$C^*$$-Algebras
%A Sal Moslehian, Mohammad
%A Najafi, Hamed
%A Mohsen Kian
%J Bulletin of the Malaysian Mathematical Sciences Society
%@ 0126-6705
%D 2019
