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Proceedings of the American Mathematical Society

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Uniform factorization for compact
sets of operators

Authors: R. Aron, M. Lindström, W. M. Ruess and R. Ryan
Journal: Proc. Amer. Math. Soc. 127 (1999), 1119-1125
MSC (1991): Primary 46B07; Secondary 46B28, 46G20, 47A68
MathSciNet review: 1473654
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Abstract: We prove a factorization result for relatively compact subsets of compact operators using the Bartle and Graves Selection Theorem, a characterization of relatively compact subsets of tensor products due to Grothendieck, and results of Figiel and Johnson on factorization of compact operators. A further proof, essentially based on the Banach-Dieudonné Theorem, is included. Our methods enable us to give an easier proof of a result of W.H. Graves and W.M. Ruess.

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Additional Information

R. Aron
Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44240

M. Lindström
Affiliation: Department of Mathematics, Åbo Akademi University, FIN-20500 Åbo, Finland

W. M. Ruess
Affiliation: Fachbereich Mathematik, Universität Essen, D-45117 Essen, Germany

R. Ryan
Affiliation: Department of Mathematics, University College Galway, Galway, Ireland
Email: Ray.Ryan@UCG.IE

Keywords: Banach spaces, compact factorization, tensor products, Michael's selection theorem, Banach-Dieudonn\'e theorem
Received by editor(s): July 25, 1997
Additional Notes: This note was written while the second and the fourth authors were visiting Kent State University to which thanks are acknowledged. The research of Mikael Lindström was supported by a grant from the Foundation of Åbo Akademi University Research Institute.
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1999 American Mathematical Society