Uniform factorization for compact sets of operators

R. Aron; M. Lindström; W. M. Ruess; R. Ryan

doi:10.1090/s0002-9939-99-04619-5

Uniform factorization for compact sets of operators

R. Aron^*, M. Lindström, W. M. Ruess, R. Ryan

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › Scientific › peer-review

9 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1119-1125
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	127
Issue number	4
DOIs	https://doi.org/10.1090/s0002-9939-99-04619-5
Publication status	Published - 1999
MoE publication type	A1 Journal article-refereed

Keywords

Banach spaces
Banach-Dieudonné
Compact factorization
Michael's selection theorem
Tensor products
Theorem

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10.1090/s0002-9939-99-04619-5

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T1 - Uniform factorization for compact sets of operators

AU - Aron, R.

AU - Lindström, M.

AU - Ruess, W. M.

AU - Ryan, R.

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AB - 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.

KW - Banach spaces

KW - Banach-Dieudonné

KW - Compact factorization

KW - Michael's selection theorem

KW - Tensor products

KW - Theorem

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U2 - 10.1090/s0002-9939-99-04619-5

DO - 10.1090/s0002-9939-99-04619-5

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EP - 1125

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

Uniform factorization for compact sets of operators

Abstract

Keywords

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