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${{C}^{*}}$-Algebras and Factorization Through Diagonal Operators

Published online by Cambridge University Press:  20 November 2018

Narcisse Randrianantoanina
Narcisse Randrianantoanina*
Affiliation:
Department of Mathematics and Statistics Miami University Oxford, Ohio 45056, e-mail: randrin@muohio.edu
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Abstract

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Let $\mathcal{A}$ be a ${{C}^{*}}$-algebra and $E$ be a Banach space with the Radon-Nikodym property. We prove that if $j$ is an embedding of $E$ into an injective Banach space then for every absolutely summing operator $T:\,\mathcal{A}\,\to \,E$, the composition $j\,\circ \,T$ factors through a diagonal operator from ${{l}^{2}}$ into ${{l}^{1}}$. In particular, $T$ factors through a Banach space with the Schur property. Similarly, we prove that for $2\,<\,p\,<\,\infty $, any absolutely summing operator from $\mathcal{A}$ into $E$ factors through a diagonal operator from ${{l}^{p}}$ into ${{l}^{2}}$.

Keywords

46L5047D15C*-algebrassumming operatorsdiagonal operatorsRadon-Nikodym property
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 4 , 01 December 2004 , pp. 615 - 623
Copyright
Copyright © Canadian Mathematical Society 2004

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