Compact range property and operators on C^*-algebras

2000/04/24 by Narcisse Randrianantoanina, Randrianantoanina, Narcisse
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Holomorphic and Operator Theory #math.FA

paper · pdf · doi:10.48550/arxiv.math/0004145

8 pages

arxiv created 2000/04/24 · arxiv updated 2009/11/30

Abstract

We prove that a Banach space E has the compact range property (CRP) if and only if for any given C^*-algebra \cal A, every absolutely summing operator from \cal A into E is compact.

Related

• Absolutely Summing Operators on non commutative C^*-algebras and applications
• Operator p-compact mappings
• Self-induced compactness in Banach spaces
• Geometric essence of "compact" operators on Hilbert C^*-modules
• Extension of p-compact operators in Banach spaces