Separation theorems for bounded convex sets of bounded operators

2024/05/27 by Mikaël Pichot, Pichot, Mikaël, Erik Séguin +1
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2405.17614

openalex publication_date 2024/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish new metric characterizations for the norm (respectively, ultraweak) closure of the convex hull of a bounded set in an arbitrary C^*-algebra (respectively, von Neumann algebra), and provide applications of these results to the majorization theory.

Related

• Majorization in C*-algebras
• A solution to Haagerup's problem and positive Hahn-Banach separation theorems in operator algebras
• Bounded elements of C*-inductive locally convex spaces
• Convex hulls of unitary orbits of normal elements in C^*-algebras with tracial rank zero
• Convex Sets Associated to C*-Algebras