Compact range property and operators on $\boldsymbol C^{\boldsymbol *}$-algebras
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- by Narcisse Randrianantoanina PDF
- Proc. Amer. Math. Soc. 129 (2001), 865-871 Request permission
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.References
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Additional Information
- Narcisse Randrianantoanina
- Affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
- Email: randrin@muohio.edu
- Received by editor(s): April 27, 1999
- Received by editor(s) in revised form: June 1, 1999
- Published electronically: September 20, 2000
- Additional Notes: The author was supported in part by NSF Grant DMS-9703789
- Communicated by: Dale Alspach
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 865-871
- MSC (1991): Primary 46L50, 47D15
- DOI: https://doi.org/10.1090/S0002-9939-00-05719-1
- MathSciNet review: 1802004