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A simple proof that super-reflexive spaces are $K$-spaces


Author: Félix Cabello Sánchez
Journal: Proc. Amer. Math. Soc. 132 (2004), 697-698
MSC (2000): Primary 46B03, 46B08, 39B82
DOI: https://doi.org/10.1090/S0002-9939-03-07180-6
Published electronically: September 29, 2003
MathSciNet review: 2019945
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Abstract: We demonstrate the title.


References [Enhancements On Off] (What's this?)

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  • 4. N. Kalton and J. W. Roberts, Uniformly exhaustive submeasures and nearly additive set functions, Trans. Amer. Math. Soc. 278 (1983) 803-816. MR 85f:28006
  • 5. M. Ribe, Examples for the nonlocally convex three space problem. Proc. Amer. Math. Soc. 73 (1979) 351-355. MR 81a:46010
  • 6. J. W. Roberts, A nonlocally convex $F$-space with the Hahn-Banach approximation property, in: Banach spaces of analytic functions, Springer Lecture Notes in Mathematics 604, Berlin-Heidelberg-New York (1977) 76-81. MR 58:30008
  • 7. B. Sims, ``Ultra''-techniques in Banach space theory. Queen's Papers in Pure and Applied Mathematics 60, Queen's University, Kingston, Ontario, Canada, 1982. MR 86h:46032

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Additional Information

Félix Cabello Sánchez
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071 Badajoz, Spain
Email: fcabello@unex.es

DOI: https://doi.org/10.1090/S0002-9939-03-07180-6
Keywords: $K$-space, super-reflexivity, ultraproduct
Received by editor(s): June 20, 2001
Published electronically: September 29, 2003
Additional Notes: Supported in part by DGICYT project BMF 2001—083.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2003 American Mathematical Society

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