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An elementary proof of the principle
of local reflexivity


Author: Antonio Martínez-Abejón
Journal: Proc. Amer. Math. Soc. 127 (1999), 1397-1398
MSC (1991): Primary 46B20, 46B10
DOI: https://doi.org/10.1090/S0002-9939-99-04687-0
Published electronically: January 28, 1999
MathSciNet review: 1476378
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Abstract | References | Similar Articles | Additional Information

Abstract: We give an elementary proof of the principle of local reflexivity.


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

  • 1. D.W. Dean, The equation $L(E,X^{**})= L(E,X)^{**}$ and the principle of local reflexivity. Proc. of Amer. Math. Soc. 40 (1973), 146-148. MR 48:2735
  • 2. W.B. Johnson, H. Rosenthal and M. Zippin, On bases, finite dimensional decompositions and weaker structures in Banach spaces. Israel J. Math. 9 (1971), 488-506. MR 43:6702
  • 3. J. Lindenstrauss and H. Rosenthal, The $\mathcal{L}_p$ spaces. Israel J. Math. 7 (1969), 325-349.
  • 4. C. Stegall, A proof of the principle of local reflexivity. Proc. of Amer. Math. Soc. 78 (1980) 154-156. MR 81e:46012

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Additional Information

Antonio Martínez-Abejón
Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712
Address at time of publication: Facultad de Ciencias, c/ Calvo Sotelo s.n., Universidad de Oviedo, Spain
Email: ama@pinon.cu.uniovi.es

DOI: https://doi.org/10.1090/S0002-9939-99-04687-0
Keywords: Local reflexivity, weak$^*$-topology, $\varepsilon$-isometry
Received by editor(s): September 27, 1996
Received by editor(s) in revised form: August 18, 1997
Published electronically: January 28, 1999
Additional Notes: The author’s research was supported by a postdoctoral Grant of the Ministry of Spain for Education and Science and DGYCIT Grant PB 94–1052 (Spain)
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society

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