On infinite dimensional uniform smoothness of Banach spaces

Stanisław Prus

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 1, page 97-105
  • ISSN: 0010-2628

Abstract

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An infinite dimensional counterpart of uniform smoothness is studied. It does not imply reflexivity, but we prove that it gives some l p -type estimates for finite dimensional decompositions, weak Banach-Saks property and the weak fixed point property.

How to cite

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Prus, Stanisław. "On infinite dimensional uniform smoothness of Banach spaces." Commentationes Mathematicae Universitatis Carolinae 40.1 (1999): 97-105. <http://eudml.org/doc/248424>.

@article{Prus1999,
abstract = {An infinite dimensional counterpart of uniform smoothness is studied. It does not imply reflexivity, but we prove that it gives some $l_p$-type estimates for finite dimensional decompositions, weak Banach-Saks property and the weak fixed point property.},
author = {Prus, Stanisław},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Banach space; nearly uniform smoothness; finite dimensional decomposition; Banach-Saks property; fixed point property; Banach space; nearly uniform smoothness; finite-dimensional decomposition; Banach-Saks property; fixed point property},
language = {eng},
number = {1},
pages = {97-105},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On infinite dimensional uniform smoothness of Banach spaces},
url = {http://eudml.org/doc/248424},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Prus, Stanisław
TI - On infinite dimensional uniform smoothness of Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 1
SP - 97
EP - 105
AB - An infinite dimensional counterpart of uniform smoothness is studied. It does not imply reflexivity, but we prove that it gives some $l_p$-type estimates for finite dimensional decompositions, weak Banach-Saks property and the weak fixed point property.
LA - eng
KW - Banach space; nearly uniform smoothness; finite dimensional decomposition; Banach-Saks property; fixed point property; Banach space; nearly uniform smoothness; finite-dimensional decomposition; Banach-Saks property; fixed point property
UR - http://eudml.org/doc/248424
ER -

References

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  14. Prus S., Nearly uniformly smooth Banach spaces, Boll. U.M.I. (7) 3-B (1989), 507-521. (1989) MR1010520
  15. Prus S., Banach spaces and operators which are nearly uniformly convex, to appear. Zbl0886.46017MR1444685
  16. Rosenthal H.P., A characterization of Banach spaces containing l 1 , Proc. Nat. Acad. Sci. (USA) 71 (1974), 2411-2413. (1974) Zbl0297.46013MR0358307
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