On the duality between Diameter Two Properties and Ideals in Banach Spaces

2025/07/25 by Sudeshna Basu, Basu, Sudeshna
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2507.18981

openalex publication_date 2025/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the dual of an M ideal of a Banach space inherits all the versions of w^* diameter two properties. We give a counter example to show that the converse is not true. We use these results to explore these properties in C(K) spaces and its duals.

Citations

• Stability Results Of Small Diameter Properties In Banach Spaces
• Stability results of octahedrality in tensor product spaces
• Extreme differences between weakly open subsets and convex combinations of slices in Banach spaces
• Octahedral norms and convex combination of slices in Banach spaces
• Big slices versus big relatively weakly open subsets in Banach spaces

Related

• Small Diameter Properties In Ideals of Banach Spaces
• On duality of diameter 2 properties
• Stability of diametral diameter two properties
• Diameter two properties in James spaces
• Stability Results Of Small Diameter Properties In Banach Spaces