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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Compact sets of compact operators in absence of $l^{1}$


Author: Fernando Mayoral
Journal: Proc. Amer. Math. Soc. 129 (2001), 79-82
MSC (2000): Primary 47B07, 46B25
Published electronically: September 14, 2000
MathSciNet review: 1784015
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Abstract:

We characterize the compactness of a subset of compact operators between Banach spaces when the domain space does not have a copy of $l^{1}.$


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Additional Information

Fernando Mayoral
Affiliation: Departamento de Matemática Aplicada II, Escuela Superior de Ingenieros, Camino de los Descubrimientos s/n 41092, Sevilla, Spain
Email: mayoral@cica.es

DOI: http://dx.doi.org/10.1090/S0002-9939-00-06007-X
PII: S 0002-9939(00)06007-X
Keywords: Compact operators, weak-Cauchy sequences, Ascoli's theorem
Received by editor(s): April 20, 1998
Published electronically: September 14, 2000
Additional Notes: This research has been partially supported by the DGESIC project no. PB97-0706 and by La Consejería de Educación y Ciencia de La Junta de Andalucia.
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society