Article
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Operator Jensen's Inequality for Operator Superquadratic Functions
Version 1
: Received: 15 December 2019 / Approved: 16 December 2019 / Online: 16 December 2019 (06:16:45 CET)
How to cite: Alomari, M. W. Operator Jensen's Inequality for Operator Superquadratic Functions. Preprints 2019, 2019120206. https://doi.org/10.20944/preprints201912.0206.v1 Alomari, M. W. Operator Jensen's Inequality for Operator Superquadratic Functions. Preprints 2019, 2019120206. https://doi.org/10.20944/preprints201912.0206.v1
Abstract
In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. Equivalent statements of a non-commutative version of Jensen's inequality for operator superquadratic function are established. A generalization of the main result to any positive unital linear map is also provided.
Keywords
operator supequadratic; operator convex; selfadjoint; Jensen 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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