Geodesic
Normal structure and fixed point property
Glasgow mathematical journal, Tome 38 (1996) no. 1, pp. 29-37

Voir la notice de l'article provenant de la source Cambridge University Press

The most classical sufficient condition for the fixed point property of non-expansive mappings FPP in Banach spaces is the normal structure (see [6] and [10]). (See definitions below). Although the normal structure is preserved under finite lp-product of Banach spaces, (1<p≤∞), (see Landes, [12], [13]), not too many positive results are known about the normal structure of an l1,-product of two Banach spaces with this property. In fact, this question was explicitly raised by T. Landes [12], and M. A. Khamsi [9] and T. Domíinguez Benavides [1] proved partial affirmative answers. Here we give wider conditions yielding normal structure for the product X1⊗1X2. 
García-Falset, J.; Lloréns-Fuster, E. Normal structure and fixed point property. Glasgow mathematical journal, Tome 38 (1996) no. 1, pp. 29-37. doi: 10.1017/S0017089500031220
@article{10_1017_S0017089500031220,
     author = {Garc{\'\i}a-Falset, J. and Llor\'ens-Fuster, E.},
     title = {Normal structure and fixed point property},
     journal = {Glasgow mathematical journal},
     pages = {29--37},
     year = {1996},
     volume = {38},
     number = {1},
     doi = {10.1017/S0017089500031220},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500031220/}
}
TY  - JOUR
AU  - García-Falset, J.
AU  - Lloréns-Fuster, E.
TI  - Normal structure and fixed point property
JO  - Glasgow mathematical journal
PY  - 1996
SP  - 29
EP  - 37
VL  - 38
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500031220/
DO  - 10.1017/S0017089500031220
ID  - 10_1017_S0017089500031220
ER  - 
%0 Journal Article
%A García-Falset, J.
%A Lloréns-Fuster, E.
%T Normal structure and fixed point property
%J Glasgow mathematical journal
%D 1996
%P 29-37
%V 38
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500031220/
%R 10.1017/S0017089500031220
%F 10_1017_S0017089500031220

[1] 1.Benavides, T. Domíinguez, Weak uniform normal structure in direct sum spaces. Studia Math. 103,(3), (1992), 283–290. Google Scholar | DOI

[2] 2.Benavides, T. Domínguez, Acedo, G. Lóopez and Xu, H. K., Weak uniform normal structure and construction fixed points of nonexpansive mappings. Preprint. Google Scholar

[3] 3.van Dulst, D. and Sims, B., Fixed points of nonexpansive mappings and Chebyshev centers in Banach space with norms of type (KK) in Banach Space Theory and Its Applications (Bucharest, 1981), Lecture Notes in Math. 991 (Springer-Verlag, 1983), 35–43. Google Scholar | DOI

[4] 4.García-Falset, J., Jiménez-Melado, A. and Lloréns-Fuster, E., A characterization of normal structure in Proceedings of Second International Conference on Fixed Point Theory and Appl.Halifax, 1991, (World Scientific, Singapore, 1992), 122–129. Google Scholar

[5] 5.García-Falset, J., Jiméenez-Melado, A. and Llorens-Fuster, E., Measures of noncompactness and normal structure in Banach spaces. Studia Math. 110, (1), (1994), 1–8. Google Scholar | DOI

[6] 6.Goebel, K. and Kirk, W. A., Topics in metric fixed point theory (Cambridge University Press, 1990). Google Scholar | DOI

[7] 7.Gossez, J. P. and Dozo, E. Lami. Some geometrical properties related to the fixed-point theory for nonexpansive mappings, Pacific J. Math. 40 (1972), 565–573. Google Scholar | DOI

[8] 8.Jiménez-Melado, A., Stability of weak normal structure in James quasi reflexive space, Bull.Austral. Math. Soc. 46 (1992), 367–372. Google Scholar | DOI

[9] 9.Khamsi, M. A., Normal structure for Banach spaces with Schauder decomposition, Canad.Math. Bull. 32 (3), (1989), 344–351. Google Scholar | DOI

[10] 10.Kirk, W. A., A fixed point theorem for mappings which do not increase distances, Amer.Math. Monthly 72 (1965), 1004–1006. Google Scholar | DOI

[11] 11.Kuczumow, T., Reich, S. and Schmidt, M., A fixed point property of l product spaces, Proc.Amer. Math. Soc. 119 (2), (1993), 457–463. Google Scholar

[12] 12.Landes, T., Permanence properties of normal structure, Pacific J. Math. 110, 1, (1984), 125–143. Google Scholar | DOI

[13] 13.Landes, T., Normal structure and the sum property, Pacific J. Math. 123 (1986), 127–147. Google Scholar | DOI

[14] 14.Tingley, D., The normal structure of James quasi reflexive space, Bull. Austral. Math. Soc. 42, (1990), 95–100. Google Scholar | DOI

Cité par Sources :