Absolutely Summing Operators on Non Commutative C-algebras and Applications
نویسنده
چکیده
Let E be a Banach space that does not contain any copy of l 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 Pe lczynski. 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 additiveA∗-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.
منابع مشابه
Compact Range Property and Operators on C ∗ - Algebras
We prove that a Banach space E has the compact range property (CRP) if and only if for any given C∗-algebra A, every absolutely summing operator from A into E is compact. Related results for p-summing operators (0 < p < 1) are also discussed as well as operators on non-commutative L-spaces and C∗-summing operators.
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