Advances in Operator Theory
- Adv. Oper. Theory
- Volume 1, Number 1 (2016), 15-91.
Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces
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.
Adv. Oper. Theory, Volume 1, Number 1 (2016), 15-91.
Received: 13 October 2016
Accepted: 3 November 2016
First available in Project Euclid: 4 December 2017
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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