Measures of noncompactness and normal structure in Banach spaces

J. García-Falset; A. Jiménez-Melado; E. Lloréns-Fuster

Studia Mathematica (1994)

  • Volume: 110, Issue: 1, page 1-8
  • ISSN: 0039-3223

Abstract

top
Sufficient conditions for normal structure of a Banach space are given. One of them implies reflexivity for Banach spaces with an unconditional basis, and also for Banach lattices.

How to cite

top

García-Falset, J., Jiménez-Melado, A., and Lloréns-Fuster, E.. "Measures of noncompactness and normal structure in Banach spaces." Studia Mathematica 110.1 (1994): 1-8. <http://eudml.org/doc/216096>.

@article{García1994,
abstract = {Sufficient conditions for normal structure of a Banach space are given. One of them implies reflexivity for Banach spaces with an unconditional basis, and also for Banach lattices.},
author = {García-Falset, J., Jiménez-Melado, A., Lloréns-Fuster, E.},
journal = {Studia Mathematica},
keywords = {normal structure; nonexpansive mappings; measures of noncompactness; measures of non-compactness; normal structure of a Banach space; reflexivity; Banach spaces with an unconditional basis; Banach lattices},
language = {eng},
number = {1},
pages = {1-8},
title = {Measures of noncompactness and normal structure in Banach spaces},
url = {http://eudml.org/doc/216096},
volume = {110},
year = {1994},
}

TY - JOUR
AU - García-Falset, J.
AU - Jiménez-Melado, A.
AU - Lloréns-Fuster, E.
TI - Measures of noncompactness and normal structure in Banach spaces
JO - Studia Mathematica
PY - 1994
VL - 110
IS - 1
SP - 1
EP - 8
AB - Sufficient conditions for normal structure of a Banach space are given. One of them implies reflexivity for Banach spaces with an unconditional basis, and also for Banach lattices.
LA - eng
KW - normal structure; nonexpansive mappings; measures of noncompactness; measures of non-compactness; normal structure of a Banach space; reflexivity; Banach spaces with an unconditional basis; Banach lattices
UR - http://eudml.org/doc/216096
ER -

References

top
  1. [B] J. Banaś, On modulus of noncompact convexity and its properties, Canad. Math. Bull. 30 (1987), 186-192. Zbl0585.46011
  2. [D-S] D. van Dulst and B. Sims, Fixed points of nonexpansive mappings and Chebyshev centers in Banach spaces with norms of type (KK), in: Banach Space Theory and Its Applications, Lecture Notes in Math. 991, Springer, Berlin, 1983, 35-43. Zbl0512.46015
  3. [G-J-L] J. García-Falset, A. Jiménez-Melado and E. Lloréns-Fuster, A characterization of normal structure, in: Proc. Second Internat. Conf. Fixed Point Theory and Appl., Halifax, 1991, K. K. Tan (ed.), World Sci., Singapore, 1992, 122-129. 
  4. [G-K] K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Stud. Adv. Math. 28, Cambridge Univ. Press, 1990. 
  5. [G-S] K. Goebel and T. Sękowski, The modulus of noncompact convexity, Ann. Univ. Mariae Curie-Skłodowska 38 (1984), 41-48. Zbl0607.46011
  6. [G-LD] J. P. Gossez and E. Lami Dozo, Some geometrical properties related to the fixed-point theory for nonexpansive mappings, Pacific J. Math. 40 (1972), 565-573. Zbl0223.47025
  7. [H] R. Huff, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), 743-749. Zbl0505.46011
  8. [K] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-1006,. Zbl0141.32402
  9. [KU] D. N. Kutzarova, Every (β)-space has the Banach-Saks property, C. R. Acad. Bulgare Sci. 42 (11) (1989), 9-11. Zbl0696.46016
  10. [L-Tz] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I-II, Springer, 1977. Zbl0362.46013
  11. [L] T. Landes, Normal structure and the sum property, Pacific J. Math. 123 (1986), 127-147. Zbl0629.46016
  12. [M] V. Montesinos, Drop property equals reflexivity, Studia Math. 87 (1987), 93-100. Zbl0652.46009
  13. [N-S-W] J. L. Nelson, K. L. Singh and J. H. M. Whitfield, Normal structures and nonexpansive mappings in Banach spaces, in: Nonlinear Analysis, Th. M. Rhassias (ed.), World Sci., Singapore, 1987, 433-492. 
  14. [R1] S. Rolewicz, On drop property, Studia Math. 85 (1987), 27-35. 
  15. [R2] S. Rolewicz, On Δ-uniform convexity and drop property, ibid. 87 (1987), 181-191. 
  16. [S] B. Sims, Fixed points of nonexpansive maps on weak and weak*-compact sets, Queen's Univ. of Kingston Lecture Notes, 1982. 

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.