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A short proof of a characterization
of reflexivity of James


Author: Eve Oja
Journal: Proc. Amer. Math. Soc. 126 (1998), 2507-2508
MSC (1991): Primary 46B20
DOI: https://doi.org/10.1090/S0002-9939-98-04691-7
MathSciNet review: 1476382
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Abstract | References | Similar Articles | Additional Information

Abstract: A short direct proof is given to a well-known intrinsic characterization of reflexivity due to R. C. James.


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

  • 1. Bernard Beauzamy, Introduction to Banach spaces and their geometry, North-Holland Mathematics Studies, vol. 68, North-Holland Publishing Co., Amsterdam-New York, 1982. Notas de Matemática [Mathematical Notes], 86. MR 670943
  • 2. Sylvie Guerre-Delabrière, Classical sequences in Banach spaces, Monographs and Textbooks in Pure and Applied Mathematics, vol. 166, Marcel Dekker, Inc., New York, 1992. With a foreword by Haskell P. Rosenthal. MR 1197117
  • 3. R. Haller and E. Oja, Geometric characterizations of positions of Banach spaces in their biduals, Arch. Math. 69 (1997), 227-233. CMP 97:16
  • 4. Robert C. James, Weak compactness and reflexivity, Israel J. Math. 2 (1964), 101–119. MR 0176310, https://doi.org/10.1007/BF02759950
  • 5. V. D. Milman, Geometric theory of Banach spaces. II. Geometry of the unit ball, Uspehi Mat. Nauk 26 (1971), no. 6(162), 73–149 (Russian). MR 0420226

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Additional Information

Eve Oja
Affiliation: Faculty of Mathematics, Tartu University, Vanemuise 46, EE2400 Tartu, Estonia
Email: eveoja@math.ut.ee

DOI: https://doi.org/10.1090/S0002-9939-98-04691-7
Received by editor(s): June 20, 1997
Received by editor(s) in revised form: August 27, 1997
Communicated by: Dale Alspach
Article copyright: © Copyright 1998 American Mathematical Society