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February 2016 Geometric mean and norm Schwarz inequality
Tsuyoshi Ando
Ann. Funct. Anal. 7(1): 1-8 (February 2016). DOI: 10.1215/20088752-3158073

Abstract

Positivity of a 2×2 operator matrix [ABBC]0 implies ACB for operator norm . This can be considered as an operator version of the Schwarz inequality. In this situation, for A,C0, there is a natural notion of geometric mean AC, for which ACAC. In this paper, we study under what conditions on A, B, and C or on B alone the norm inequality ACB can be improved as ACB.

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Tsuyoshi Ando. "Geometric mean and norm Schwarz inequality." Ann. Funct. Anal. 7 (1) 1 - 8, February 2016. https://doi.org/10.1215/20088752-3158073

Information

Received: 5 December 2014; Accepted: 17 December 2014; Published: February 2016
First available in Project Euclid: 15 October 2015

zbMATH: 1339.47022
MathSciNet: MR3449334
Digital Object Identifier: 10.1215/20088752-3158073

Subjects:
Primary: 47A64
Secondary: 47A30, 47A63, 47B15

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.7 • No. 1 • February 2016
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