On an extension of norms from a subspace to the whole Banach space keeping their rotundity

M. Fabian

Studia Mathematica (1995)

  • Volume: 112, Issue: 3, page 203-211
  • ISSN: 0039-3223

Abstract

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Let ℛ denote some kind of rotundity, e.g., the uniform rotundity. Let X admit an ℛ-norm and let Y be a reflexive subspace of X with some ℛ-norm ∥·∥. Then we are able to extend ∥·∥ from Y to an ℛ-norm on X.

How to cite

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Fabian, M.. "On an extension of norms from a subspace to the whole Banach space keeping their rotundity." Studia Mathematica 112.3 (1995): 203-211. <http://eudml.org/doc/216148>.

@article{Fabian1995,
abstract = {Let ℛ denote some kind of rotundity, e.g., the uniform rotundity. Let X admit an ℛ-norm and let Y be a reflexive subspace of X with some ℛ-norm ∥·∥. Then we are able to extend ∥·∥ from Y to an ℛ-norm on X.},
author = {Fabian, M.},
journal = {Studia Mathematica},
keywords = {LUR norm; uniform rotundity},
language = {eng},
number = {3},
pages = {203-211},
title = {On an extension of norms from a subspace to the whole Banach space keeping their rotundity},
url = {http://eudml.org/doc/216148},
volume = {112},
year = {1995},
}

TY - JOUR
AU - Fabian, M.
TI - On an extension of norms from a subspace to the whole Banach space keeping their rotundity
JO - Studia Mathematica
PY - 1995
VL - 112
IS - 3
SP - 203
EP - 211
AB - Let ℛ denote some kind of rotundity, e.g., the uniform rotundity. Let X admit an ℛ-norm and let Y be a reflexive subspace of X with some ℛ-norm ∥·∥. Then we are able to extend ∥·∥ from Y to an ℛ-norm on X.
LA - eng
KW - LUR norm; uniform rotundity
UR - http://eudml.org/doc/216148
ER -

References

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  1. [1] J. M. Borwein and M. Fabian, On convex functions having points of Gateaux differentiability which are not points of Fréchet differentiability, a preprint. Zbl0793.46021
  2. [2] J. M. Borwein, M. Fabian and J. Vanderwerff, Locally Lipschitz functions and bornological derivatives, a preprint. Zbl0920.46004
  3. [3] J. Diestel, Geometry of Banach Spaces-Selected Topics, Lecture Notes in Math. 485, Springer, 1975. Zbl0307.46009
  4. [4] R. Deville, G. Godefroy and V. E. Zizler, Smoothness and Renormings in Banach Spaces, Pitman Monographs in Pure and Appl. Math. 64, Wiley, New York, 1993. Zbl0782.46019
  5. [5] K. John and V. Zizler, On extension of rotund norms, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 705-707. Zbl0344.46048
  6. [6] K. John and V. Zizler, On extension of rotund norms II, Pacific J. Math. 82 (1979), 451-455. Zbl0444.46014
  7. [7] V. E. Zizler, Smooth extension of norms and complementability of subspaces, Arch. Math. (Basel) 53 (1989), 585-589. Zbl0662.46023

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