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Uniform factorization for compact sets of operators |
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| Authors: | R Aron M Lindströ m W M Ruess R Ryan |
| Institution: | Department of Mathematics, Kent State University, Kent, Ohio 44240 ; Department of Mathematics, Åbo Akademi University, FIN-20500 Åbo, Finland ; Fachbereich Mathematik, Universität Essen, D-45117 Essen, Germany ; Department of Mathematics, University College Galway, Galway, Ireland |
| 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. |
| Keywords: | Banach spaces compact factorization tensor products Michael's selection theorem Banach-Dieudonn\'e theorem |
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