Reflexivity, contraction functions and minimum-norm elements

A. Aizpuru; F. J. García-Pacheco

doi:10.1556/sscmath.42.2005.4.7

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 42: Issue 4

Reflexivity, contraction functions and minimum-norm elements

Authors:

A. Aizpuru

A. Aizpuru

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F. J. García-Pacheco

F. J. García-Pacheco

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Pages:: 431–443

Online Publication Date:: 07 Nov 2005

Publication Date:: 01 Oct 2005

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.42.2005.4.7

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Here we present a new proof of Blatter's result: a normed space is complete if every bounded closed convex subset has an element of minimum norm. We also present geometrical conditions for the existence of minimum-norm elements in bounded closed convex sets. Also, we characterize reflexivity in the class of Banach spaces by means of contraction functions. Furthermore, we study what happens if we remove the completeness hypothesis.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

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András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
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