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Lobachevskii Journal of Mathematics

, Volume 39, Issue 9, pp 1287–1292 | Cite as

An Inequality for Projections and Convex Functions

  • Sami Abdullah AbedEmail author
Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
  • 8 Downloads

Abstract

We propose the conditions for a continuous function to be projection-convex, i.e. f(λp+ (1 − λ)q) ≤ λf(p) + (1 − λ)f(q) for any projections p and q and any real λ ∈ (0, 1). Also we obtain the characterization of projections commutativity and the characterization of trace in terms of equalities for non-flat functions.

Keywords and phrases

Hilbert space von Neumann algebra projection measure space commutativity convex function operator inequality 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazan, TatarstanRussia

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