Generalizations of refined Young inequalities and reverse inequalities for τ-measurable operators

ABSTRACT

In this paper, we present some generalizations of refinements of Young inequalities and reverse inequalities due to Furuichi, Choi as well as Manasrah and Kittaneh to cases of τ-measurable operators. Among other things, refined Young-type inequalities for operator traces, determinants and p-norms of positive τ-measurable operators are also provided.

COMMUNICATED BY:

• Rajesh Pereira

KEYWORDS:

• von Neumann algebras
• positive τ-measurable operators
• Young inequality
• reverse inequality
• determinant

2000 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 46L52
• 47A63

Acknowledgments

The author is grateful to the editor and the anonymous referee for making helpful comments and suggestions which have been incorporated into this version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China [grant number 11701255].