Factorization of weakly compact operators between Banach spaces and Fréchet or (LB)-spaces

Authors

  • José Bonet Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universidad Politécnica de Valencia, E-46071 Valencia, Spain Author
  • J.D. Maitland Wright Mathematical Institute, University of Aberdeen, Aberdeen AB24 3FX, Scotland, UK Author

Keywords:

Weakly compact operators, reflexive operators, factorization, reflexive Banach spaces, (LB)-spaces, Fréchet spaces

Subjects:

46A04, 46A03, 46A25, 46B10, 47B07

Abstract

In this note we show that weakly compact operators from a Banachspace $X$ into a complete (LB)-space $E$ need not factorizethrough a reflexive Banach space. If $E$ is a Fréchet space,then weakly compact operators from a Banach space $X$ into $E$factorize through a reflexive Banach space. The factorization ofoperators from a Fréchet or a complete (LB)-space into a Banachspace mapping bounded sets into relatively weakly compact sets isalso investigated.

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Published

2012-10-15

Issue

Vol. 64 No. 4 (2012): Vol. 64, Issue 4

Section

Articles

License

Copyright (c) 2012 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.