Minimal and Maximal Operator Space Structures on Banach Spaces

TL;DR

This paper explores the properties of minimal and maximal operator space structures on Banach spaces, focusing on their subspace and quotient space structures, and clarifies their extremal roles in operator space theory.

Contribution

It analyzes how minimal and maximal operator space structures behave under subspace and quotient operations, extending the understanding of their extremal properties.

Findings

Characterization of subspace structures of Min and Max

Analysis of quotient space structures of Min and Max

Extension of extremal properties to subspaces and quotients

Abstract

Given a Banach space $X$, there are many operator space structures possible on $X$, which all have $X$ as their first matrix level. Blecher and Paulsen identified two extreme operator space structures on $X$, namely $Min(X)$ and $Max(X)$ which represents respectively, the smallest and the largest operator space structures admissible on $X$. In this note, we consider the subspace and the quotient space structure of minimal and maximal operator spaces.