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The classical renorming theorems

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Geometry of Banach Spaces-Selected Topics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 485))

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References

  1. E. Asplund, Averaged norms, Israel J. Math. 5 (1967), 227–233.

    Article  MathSciNet  MATH  Google Scholar 

  2. -, Frechet differentiability of convex functions, Acta Math., 121 (1968), 31–48.

    Article  MathSciNet  MATH  Google Scholar 

  3. R. Bonic and J. Frampton, Smooth functions on Banach manifolds, J. Math. and Mech., 15 (1966), 877–898.

    MathSciNet  MATH  Google Scholar 

  4. J. A. Clarkson, Uniformly convex spaces, Trans. AMS, 40 (1936), 396–414.

    Article  MathSciNet  MATH  Google Scholar 

  5. F. K. Dashiell and J. Lindenstrauss, Some examples concerning strictly convex norms on C(K) spaces, Israel J. Math., 16 (1973), 329–342.

    Article  MathSciNet  MATH  Google Scholar 

  6. W. J. Davis and W. B. Johnson, A renorming of non-reflexive Banach spaces, Proc. AMS, 37 (1973), 386–489.

    MathSciNet  Google Scholar 

  7. M. M. Day, Strict convexity and smoothness, Trans. AMS, 78 (1955), 516–528.

    Article  MathSciNet  MATH  Google Scholar 

  8. -, Every L-space is isomorphic to a strictly convex space, Proc. AMS, 8 (1957), 415–417.

    MathSciNet  MATH  Google Scholar 

  9. -, A geometric proof of Asplund's differentiability theorem, Israel J. Math., 13 (1972), 277–280.

    Article  MathSciNet  Google Scholar 

  10. M. I. Kadec, On weak and norm convergence, Dokl. Akad. Nauk SSSR, 122 (1958), 13–16 (Russian).

    MathSciNet  Google Scholar 

  11. -, A proof of the topological equivalence of all separable infinite dimensional Banach spaces, Funckional Anal. i Prilozen, 1 (1967), 53–62 (Russian).

    Article  MathSciNet  Google Scholar 

  12. V. L. Klee, Convex bodies and periodic homeomorphisms in Hilbert space, Trans. AMS, 74 (1953), 10–43.

    Article  MathSciNet  MATH  Google Scholar 

  13. -, Mappings into normed linear spaces, Func. Math., 49 (1960), 25–34.

    MathSciNet  MATH  Google Scholar 

  14. J. Lindenstrauss, Weakly compact sets-their topological properties and the Banach spaces they generate, Ann. of Math. Studies, 69 (1972), 235–273.

    MathSciNet  MATH  Google Scholar 

  15. J. Rainwater, Local uniform convexity of Day's norm on c0 (Γ), Proc. AMS, 22 (1969), 335–339.

    MathSciNet  MATH  Google Scholar 

  16. D. G. Tacon, The conjugate of a smooth Banach space, Bull. Australian Math. Soc., 2 (1970), 415–425.

    Article  MathSciNet  MATH  Google Scholar 

  17. S. Troyanski, On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia Math., 37 (1971), 173–180.

    MathSciNet  MATH  Google Scholar 

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© 1975 Springer-Verlag

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Diestel, J. (1975). The classical renorming theorems. In: Geometry of Banach Spaces-Selected Topics. Lecture Notes in Mathematics, vol 485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082083

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  • DOI: https://doi.org/10.1007/BFb0082083

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  • Print ISBN: 978-3-540-07402-1

  • Online ISBN: 978-3-540-37913-3

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