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

Silvestru Sever Dragomir

#### 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
Accepted: 3 November 2016
First available in Project Euclid: 4 December 2017

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

#### 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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