Article
Version 1
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Trace Operator Inequality for Superquadratic Functions
Version 1
: Received: 13 December 2019 / Approved: 15 December 2019 / Online: 15 December 2019 (14:08:32 CET)
Version 2 : Received: 11 January 2020 / Approved: 12 January 2020 / Online: 12 January 2020 (17:55:39 CET)
Version 2 : Received: 11 January 2020 / Approved: 12 January 2020 / Online: 12 January 2020 (17:55:39 CET)
How to cite: Alomari, M. Trace Operator Inequality for Superquadratic Functions. Preprints 2019, 2019120192. https://doi.org/10.20944/preprints201912.0192.v1 Alomari, M. Trace Operator Inequality for Superquadratic Functions. Preprints 2019, 2019120192. https://doi.org/10.20944/preprints201912.0192.v1
Abstract
In this work, some operator trace inequalities are proved. An extension of Klein's inequality for all Hermitian matrices is proved. A non-commutative version (or Hansen-Pedersen version) of the Jensen trace inequality is provided as well. A generalization of the result for any positive Hilbert space operators acts on a positive unital linear map is established.
Keywords
Klein's inequality; Jensen's trace inequality; trace inequality
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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The commenter has declared there is no conflict of interests.
There is an updated version of this manuscript. A corrected version of the first two results is pointed out.