Uniform factorization for compact sets of operators
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- by R. Aron, M. Lindström, W. M. Ruess and R. Ryan PDF
- Proc. Amer. Math. Soc. 127 (1999), 1119-1125 Request permission
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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Additional Information
- R. Aron
- Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44240
- MR Author ID: 27325
- 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
- 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 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1119-1125
- MSC (1991): Primary 46B07; Secondary 46B28, 46G20, 47A68
- DOI: https://doi.org/10.1090/S0002-9939-99-04619-5
- MathSciNet review: 1473654