Holder's inequality for roots of symmetric operator spaces

TL;DR

This paper establishes a version of Holder's inequality with optimal constants for p-th roots of symmetric operator spaces associated with semifinite von Neumann algebras, enhancing the theoretical framework of operator space analysis.

Contribution

It introduces a Holder's inequality with a constant for symmetric operator spaces, improving understanding of their structure and properties.

Findings

Holder's inequality with constant 1 for strongly symmetric spaces

Extension of inequality to p-th roots of symmetric operator spaces

Advancement in the mathematical theory of operator spaces

Abstract

We prove a version of Holder's inequality with a constant for p-th roots of symmetric operator spaces of operators affiliated to a semifinite von Neumann algebra factor, and with constant equal to 1 for strongly symmetric operator spaces.