Absolutely Summing Operators on non commutative C^*-algebras and applications

1995/11/02 by Randrianantoanina, Narcisse
#46E #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.math/9511207

Abstract

Let E be a Banach space that does not contain any copy of ℓ¹ and \A be a non commutative C^*-algebra. We prove that every absolutely summing operator from \A into E^* is compact, thus answering a question of Pełczynski. As application, we show that if G is a compact metrizable abelian group and Λ is a Riesz subset of its dual then every countably additive \A^*-valued measure with bounded variation and whose Fourier transform is supported by Λ has relatively compact range. Extensions of the same result to symmetric spaces of measurable operators are also presented.

Related

• Compact range property and operators on C^*-algebras
• Domination of operators in the non-commutative setting
• Geometric essence of "compact" operators on Hilbert C^*-modules
• Extending representations of Banach algebras to their biduals
• A characterization of compact operators on ℓ^p-spaces