Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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 (doi: 10.20944/preprints201912.0206.v1). Alomari, M.W. Operator Jensen's Inequality for Operator Superquadratic Functions. Preprints 2019, 2019120206 (doi: 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.

Subject Areas

operator supequadratic; operator convex; selfadjoint; Jensen inequality

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