A Note on Submaximal Operator Space Structures

TL;DR

This paper characterizes the smallest submaximal operator space structure on Banach spaces, explores its universal properties, and examines duality relations, providing insights into the structure of operator spaces.

Contribution

It introduces a characterization of the minimal submaximal space structure {}(X) via a universal property and discusses its uniqueness and duality relations.

Findings

{}(X) is characterized up to complete isometric isomorphism.

Injective Banach spaces have a unique submaximal structure.

The paper explores duality relations of {}-spaces.

Abstract

In this note, we consider the smallest submaximal space structure {\mu}(X) on a Banach space X. We derive a characterization of {\mu}(X) up to complete isometric isomorphism in terms of a universal property. Also, we show that an injective Banach space has a unique submaximal space structure and we explore some duality relations of {\mu}-spaces. Key Words: operator spaces, maximal operator spaces, submaximal spaces, {\mu}- spaces.