Minimal and Maximal Operator Space Structures on Banach Spaces

2014/11/19 by Pradeep Kumar, Vinod Kumar P., P., Vinod Kumar +2
Mathematics · #46L07 #47L25 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA #msc:46L07 #msc:47L25

paper · pdf · doi:10.48550/arxiv.1411.5079

12 Pages

arxiv created 2014/11/19 · openalex publication_date 2014/11/19 · arxiv updated 2014/11/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Related

• A Note on Submaximal Operator Space Structures
• Lectures on maximal monotone operators
• A note on the maximal operator on Banach function spaces
• Recent progress on Monotone Operator Theory
• Linear structures in the set of non-norm-attaining operators on Banach spaces