%0 Journal Article
%T Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces
%J Advances in Operator Theory
%I Tusi Mathematical Research Group (TMRG)
%Z 2538-225X
%A Dragomir, Sever
%D 2016
%\ 12/01/2016
%V 1
%N 1
%P 15-91
%! Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces
%K trace class operators
%K Hilbert-Schmidt operators
%K Trace
%K Schwarz inequality
%K Kato inequality
%K Cassels inequality
%K Shisha--Mond inequality
%K Trace inequalities for matrices
%K Power series of operators
%R 10.22034/aot.1610.1032
%X In this paper, we survey some recent trace inequalities for operators inHilbert spaces that are connected to Schwarz's, Buzano's and Kato'sinequalities and the reverses of Schwarz inequality known in the literatureas Cassels' inequality and Shisha--Mond's inequality. Applications for somefunctionals that are naturally associated to some of these inequalities andfor functions of operators defined by power series are given. Examples forfundamental functions such as the power, logarithmic, resolvent andexponential functions are provided as well.
%U http://www.aot-math.org/article_38906_2284ce53f9a52e67a0bd59db77882ece.pdf