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Abstract and Applied Analysis
Volume 2015, Article ID 851568, 5 pages
http://dx.doi.org/10.1155/2015/851568
Research Article

Positivity, Betweenness, and Strictness of Operator Means

Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand

Received 5 March 2015; Accepted 7 May 2015

Academic Editor: Sergei V. Pereverzyev

Copyright © 2015 Pattrawut Chansangiam. 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.

Abstract

An operator mean is a binary operation assigned to each pair of positive operators satisfying monotonicity, continuity from above, the transformer inequality, and the fixed-point property. It is well known that there are one-to-one correspondences between operator means, operator monotone functions, and Borel measures. In this paper, we provide various characterizations for the concepts of positivity, betweenness, and strictness of operator means in terms of operator inequalities, operator monotone functions, Borel measures, and certain operator equations.