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Autumn 2016 Square inequality and strong order relation
Tsuyoshi Ando
Adv. Oper. Theory 1(1): 1-7 (Autumn 2016). DOI: 10.22034/aot.1610.1035

Abstract

It is well-known that for Hilbert space linear operators $0 \leq A$ and $0 \leq C$, inequality $C \leq A$ does not imply $C^2 \leq A^2.$ We introduce a strong order relation $0 \leq B \lll A$, which guarantees that $C^2 \leq B^{1/2}AB^{1/2}$ text for all $0 \leq C \leq B,$ and that $C^2 \leq A^2$ when $B$ commutes with $A$. Connections of this approach with the arithmetic-geometric mean inequality of Bhatia-Kittaneh as well as the Kantorovich constant of $A$ are mentioned.

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Tsuyoshi Ando. "Square inequality and strong order relation." Adv. Oper. Theory 1 (1) 1 - 7, Autumn 2016. https://doi.org/10.22034/aot.1610.1035

Information

Received: 1 October 2016; Accepted: 23 October 2016; Published: Autumn 2016
First available in Project Euclid: 4 December 2017

zbMATH: 1353.47028
MathSciNet: MR3721324
Digital Object Identifier: 10.22034/aot.1610.1035

Subjects:
Primary: 47A63
Secondary: 47A64

Keywords: Kantorovich constant , operator arithmetic-geometric mean inequality , square inequality , strong order relation

Rights: Copyright © 2016 Tusi Mathematical Research Group

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