Advances in Operator Theory

Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces

Silvestru Sever Dragomir

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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.

Article information

Source
Adv. Oper. Theory, Volume 1, Number 1 (2016), 15-91.

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

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512416208

Digital Object Identifier
doi:10.22034/aot.1610.1032

Mathematical Reviews number (MathSciNet)
MR3721326

Zentralblatt MATH identifier
1353.47030

Subjects
Primary: 47A63: Operator inequalities
Secondary: 47A99: None of the above, but in this section

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

Citation

Dragomir, Silvestru Sever. Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces. Adv. Oper. Theory 1 (2016), no. 1, 15--91. doi:10.22034/aot.1610.1032. https://projecteuclid.org/euclid.aot/1512416208


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