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Autumn 2016 Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces
Silvestru Sever Dragomir
Adv. Oper. Theory 1(1): 15-91 (Autumn 2016). DOI: 10.22034/aot.1610.1032

Abstract

In this paper, we survey some recent trace inequalities for operators in Hilbert spaces that are connected to Schwarz's, Buzano's and Kato's inequalities and the reverses of Schwarz inequality known in the literature as Cassels' inequality and Shisha-Mond's inequality. Applications for some functionals that are naturally associated to some of these inequalities and for functions of operators defined by power series are given. Examples for fundamental functions such as the power, logarithmic, resolvent and exponential functions are provided as well.

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Silvestru Sever Dragomir. "Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces." Adv. Oper. Theory 1 (1) 15 - 91, Autumn 2016. https://doi.org/10.22034/aot.1610.1032

Information

Received: 13 October 2016; Accepted: 3 November 2016; Published: Autumn 2016
First available in Project Euclid: 4 December 2017

zbMATH: 1353.47030
MathSciNet: MR3721326
Digital Object Identifier: 10.22034/aot.1610.1032

Subjects:
Primary: 47A63
Secondary: 47A99

Keywords: Cassels inequality , Hilbert-Schmidt operators , Kato inequality , power series of operators , Schwarz inequality , Shisha–Mond inequality , Trace , trace class operators , trace inequalities for matrices

Rights: Copyright © 2016 Tusi Mathematical Research Group

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