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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On $ p$-$ C\sp *$ summing operators

Author: Krzysztof Nowak
Journal: Proc. Amer. Math. Soc. 111 (1991), 657-662
MSC: Primary 47B10; Secondary 46L05
MathSciNet review: 1034881
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Abstract: We prove that every bounded linear operator $ T:A \to {C_p}(H)$ such that $ i \circ T:A \to B(H)$ is positive (where $ A$ is a unital $ {C^*}$-algebra, $ {C_p}(H)$ a Schatten class, $ i$ the identity map from $ {C_p}(H)$ into $ B(H)$ is $ p - {C^*}$ summing. This permits us to characterize $ p - {C^*}$ summing operators in some classes of multipliers.

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PII: S 0002-9939(1991)1034881-2
Keywords: $ {C^*}$-summing operator, positive operator, Schatten class
Article copyright: © Copyright 1991 American Mathematical Society