The Australian Journal of Mathematical Analysis and Applications

Home News Editors Volumes RGMIA Subscriptions Authors Contact

ISSN 1449-5910  


Paper Information

Paper Title:

Trace Inequalities for Operators in Hilbert Spaces: a Survey of Recent Results


Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University,
PO Box 14428 Melbourne City, MC 8001,

2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa


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. Further, various trace inequalities for convex functions are presented including refinements of Jensen inequality and several reverses of Jensen's inequality. Hermite-Hadamard type inequalities and the trace version of Slater's inequality are given. Some Lipschitz type inequalities are also surveyed. Examples for fundamental functions such as the power, logarithmic, resolvent and exponential functions are provided as well.

Full Text PDF:

2004-2023 Austral Internet Publishing