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2019 Improved Bellman and Aczel inequalities for operators
Fereshteh Hashemi, Ali Farokhinia
Rocky Mountain J. Math. 49(7): 2175-2183 (2019). DOI: 10.1216/RMJ-2019-49-7-2175

Abstract

We derive several more accurate operator Bellman and Aczel inequalities. Among other inequalities, it is shown that if $\Phi :\mathbb {B}( \mathscr {H} )\to \mathbb {B}( \mathscr {H})$ is a unital positive linear map, $A,B\in \mathbb {B}( \mathscr {H})$ are two contraction operators, and we take $0\le \lambda ,v\le 1$ and $p>1$, then $$ \Phi ( {{( I-A )}^{\frac {1}{p}}}{{\nabla }_{\lambda }}{{( I-B )}^{\frac {1}{p}}} ) \le {{( \Phi ( I-A{{\nabla }_{\lambda }}B ) )}^{\frac {1}{p}},} $$ which nicely improves the operator Bellman inequality.

Citation

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Fereshteh Hashemi. Ali Farokhinia. "Improved Bellman and Aczel inequalities for operators." Rocky Mountain J. Math. 49 (7) 2175 - 2183, 2019. https://doi.org/10.1216/RMJ-2019-49-7-2175

Information

Published: 2019
First available in Project Euclid: 8 December 2019

zbMATH: 07152859
MathSciNet: MR4039964
Digital Object Identifier: 10.1216/RMJ-2019-49-7-2175

Subjects:
Primary: 47A63
Secondary: 47A64.

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 7 • 2019
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