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

top
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

top

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

top
  1. Banaś J., Compactness conditions in the geometric theory of Banach spaces, Nonlinear Anal. 16 (1990), 669-682. (1990) MR1097324
  2. Banaś J., Fraczek K., Conditions involving compactness in geometry of Banach spaces, Nonlinear Anal. 20 (1993), 1217-1230. (1993) MR1219238
  3. Banaś J., Goebel K., Measures of Noncompactness in Banach Spaces, Marcel Dekker New York (1980). (1980) MR0591679
  4. van Dulst D., Reflexive and Superreflexive Banach Spaces, Mathematisch Centrum Amsterdam (1978). (1978) Zbl0412.46006MR0513590
  5. García Falset J., Stability and fixed points for nonexpansive mappings, Houston J. Math 20 (1994), 495-505. (1994) MR1287990
  6. García Falset J., The fixed point property in Banach spaces with NUS-property, preprint. 
  7. Goebel K., Sȩkowski T., The modulus of noncompact convexity, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 38 (1984), 41-48. (1984) MR0856623
  8. Huff R., Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), 743-749. (1980) Zbl0505.46011MR0595102
  9. James R.C., Bases and reflexivity of Banach spaces, Ann. of Math. 52 (1950), 518-527. (1950) Zbl0039.12202MR0039915
  10. James R.C., Uniformly non-square Banach spaces, Ann. of Math. 80 (1964), 542-550. (1964) Zbl0132.08902MR0173932
  11. James R.C., Super-reflexive spaces with bases, Pacific J. Math. 41 (1972), 409-419. (1972) Zbl0235.46031MR0308752
  12. Johnson W.B., Zippin M., On subspaces of quotients of ( G n ) l p and ( G n ) c 0 , Israel J. Math. 13 (1972), 311-316. (1972) MR0331023
  13. Lindenstrauss J., Tzafriri L., Classical Banach Spaces I. Sequence Spaces, Springer-Verlag New York (1977). (1977) Zbl0362.46013MR0500056
  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
  17. Sȩkowski T., Stachura A., Noncompact smoothness and noncompact convexity, Atti. Sem. Mat. Fis. Univ. Modena 36 (1988), 329-338. (1988) MR0976047
  18. Zippin M., A remark on bases and reflexivity in Banach spaces, Israel J. Math. 6 (1968), 74-79. (1968) Zbl0157.20101MR0236677

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.