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Uniform factorization for compact sets of operators
Author(s):
R.
Aron;
M.
Lindström;
W.
M.
Ruess;
R.
Ryan
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1119-1125.
MSC (1991):
Primary 46B07;
Secondary 46B28, 46G20, 47A68
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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.
References:
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- R. Bartle, L. Graves, Mappings between function spaces, Trans. Amer. Math. Soc. 72 (1952), 400-413 MR 13:951i
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 , Math. Ann. 220 (1976), 105-122 MR 54:8332 - [Di]
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 , Math. Ann. 208 (1974), 1-8 MR 49:3507 - [Ru1]
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- [Ru2]
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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:
10.1090/S0002-9939-99-04619-5
PII:
S 0002-9939(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
Copyright of article:
Copyright
1999,
American Mathematical Society
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