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

Document Type: Review Article

Author

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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