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COMPLEMENTED COPIES OF [ell ]2 IN SPACES OF INTEGRAL OPERATORS

Published online by Cambridge University Press:  27 July 2005

JOAQUÍN M. GUTIÉRREZ
JOAQUÍN M. GUTIÉRREZ
Affiliation:
Departamento de Matemática Aplicada, ETS de Ingenieros Industriales, Universidad Politécnica de Madrid, C. José Gutiérrez Abascal 2, 28006 Madrid (Spain) e-mail: [email protected]
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Abstract

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It is shown that, if $E$ and $F$ are Banach spaces containing complemented copies of $\ell_1$, then the space of integral operators ${\mathcal I}(E,F^*)\equiv (E\otimes_\eps F)^*$ contains a complemented copy of $\ell_2$. This answers a question of Félix Cabello and Ricardo García.

Keywords

Primary: 46B28Secondary: 46B2047L05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 2 , May 2005 , pp. 287 - 290
Copyright
2005 Glasgow Mathematical Journal Trust