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Compact range property and operators on $\boldsymbol C^{\boldsymbol*}$-algebras

Author(s): Narcisse Randrianantoanina
Journal: Proc. Amer. Math. Soc. 129 (2001), 865-871.
MSC (1991): Primary 46L50, 47D15
Posted: September 20, 2000
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Abstract:

We prove that a Banach space $E$ has the compact range property (CRP) if and only if, for any given $C^*$-algebra $\mathcal{A}$, every absolutely summing operator from $\mathcal{A}$ into $E$ is compact. Related results for $p$-summing operators ($ 0<p<1$) are also discussed as well as operators on non-commutative $L^1$-spaces and $C^*$-summing operators.

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Additional Information:

Narcisse Randrianantoanina
Affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
Email: randrin@muohio.edu

DOI: 10.1090/S0002-9939-00-05719-1
PII: S 0002-9939(00)05719-1
Keywords: $C^*$-algebras, vector measures
Received by editor(s): April 27, 1999
Received by editor(s) in revised form: June 1, 1999
Posted: September 20, 2000
Additional Notes: The author was supported in part by NSF Grant DMS-9703789
Communicated by: Dale Alspach
Copyright of article: Copyright 2000, American Mathematical Society

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