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A Riemann type theorem for series of operators on Banach spaces

Published online by Cambridge University Press:  17 April 2009

A. Aizpuru ,
A. Gutiérrez-Dávila  and
A. Sala
A. Aizpuru
Affiliation:
Departamento de Matemáticas, Universidad de Cádiz, Apdo. 40, 11510-Puerto Real (Cádiz), Spain e-mail: antonio.aizpuru@ucas.es, antonio.gutierrez@uca.esantonio.sala@uca.es
A. Gutiérrez-Dávila
Affiliation:
Departamento de Matemáticas, Universidad de Cádiz, Apdo. 40, 11510-Puerto Real (Cádiz), Spain e-mail: antonio.aizpuru@ucas.es, antonio.gutierrez@uca.esantonio.sala@uca.es
A. Sala
Affiliation:
Departamento de Matemáticas, Universidad de Cádiz, Apdo. 40, 11510-Puerto Real (Cádiz), Spain e-mail: antonio.aizpuru@ucas.es, antonio.gutierrez@uca.esantonio.sala@uca.es
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Abstract

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We study Kalton's theorem on the unconditional convergence of series of compact operators and we use some matrix techniques to obtain sufficient conditions, weaker than previous ones, on the convergence and unconditional convergence of series of compact operators. Finally, we characterise weak unconditionally Cauchy series in Cℒ(X, Y) in the terms of certain spaces of vector sequences.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 13 - 20
Copyright
Copyright © Australian Mathematical Society 2003

References

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