Journal of the Ramanujan Mathematical Society

Douglas R. Farenick ¹, S. Mahmoud Manjegani ¹

Affiliations
1 Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan S4S 0A2, CA

Abstract

Young’s inequality in two variables is formulated so as to apply to positive Hilbert space operators. The Young-type operator inequalities herein occur in the context of von Neumann algebras, and apply to the singular numbers, the spectral preorder, and traces of positive operators. As an application, a Young inequality relative to tracial states on unital C∗-algebras is obtained and, if the tracial state is faithful, the cases of equality are completely determined.

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