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 | References | Similar Articles | Additional Information

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

Email:
aron@mcs.kent.edu

**M. Lindström**

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

Email:
mlindstr@ra.abo.fi

**W. M. Ruess**

Affiliation:
Fachbereich Mathematik, Universität Essen, D-45117 Essen, Germany

Email:
mate00@sp2.power.uni-essen.de

**R. Ryan**

Affiliation:
Department of Mathematics, University College Galway, Galway, Ireland

Email:
Ray.Ryan@UCG.IE

DOI:
https://doi.org/10.1090/S0002-9939-99-04619-5

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