The modulus of near smoothness of the lp product of a sequence of Banach spaces
Glasgow mathematical journal, Tome 39 (1997) no. 2, pp. 153-165

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

In the classical geometry of Banach spaces the notions of smoothness, uniform smoothness, strict and uniform convexity introduced by Day [1] and Clarkson [2] play a very important role and are used in many branches of functional analysis ([3,4,5], for example). In recent years a lot of papers have appeared containing interesting generalizations of these notions in terms of a measure of noncompactness. These new concepts investigated in this paper as near uniform smoothness, local near uniform smoothness and modulus of near smoothness have been introduced by Stachura and Sekowski [6] and Banaś [7] (see also [8,9]).
Olszowy, Leszek. The modulus of near smoothness of the lp product of a sequence of Banach spaces. Glasgow mathematical journal, Tome 39 (1997) no. 2, pp. 153-165. doi: 10.1017/S0017089500032043
@article{10_1017_S0017089500032043,
     author = {Olszowy, Leszek},
     title = {The modulus of near smoothness of the lp product of a sequence of {Banach} spaces},
     journal = {Glasgow mathematical journal},
     pages = {153--165},
     year = {1997},
     volume = {39},
     number = {2},
     doi = {10.1017/S0017089500032043},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500032043/}
}
TY  - JOUR
AU  - Olszowy, Leszek
TI  - The modulus of near smoothness of the lp product of a sequence of Banach spaces
JO  - Glasgow mathematical journal
PY  - 1997
SP  - 153
EP  - 165
VL  - 39
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500032043/
DO  - 10.1017/S0017089500032043
ID  - 10_1017_S0017089500032043
ER  - 
%0 Journal Article
%A Olszowy, Leszek
%T The modulus of near smoothness of the lp product of a sequence of Banach spaces
%J Glasgow mathematical journal
%D 1997
%P 153-165
%V 39
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500032043/
%R 10.1017/S0017089500032043
%F 10_1017_S0017089500032043

[1] 1.Day, M. M., Uniformly convexity in factor and conjugate spaces, Ann. of Math. (2) 45 (1944), 375–385. Google Scholar | DOI

[2] 2.Clarkson, J. A., Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396–414. Google Scholar | DOI

[3] 3.Day, M. M., Normed Linear Spaces (Springer, 1973). Google Scholar | DOI

[4] 4.Kirk, W. A., Fixed point theory for nonexpansive mappings II, Contemp. Math. 18 (1983), 121–140. Google Scholar | DOI

[5] 5.Köthe, G., Topological Vector Spaces I (Springer, 1969). Google Scholar

[6] 6.Sekowski, T. and Stachura, A., Noncompact smoothness and noncompact convexity, Atti. Sem. Mat. Fis. Univ. Modena 36 (1988), 329–338. Google Scholar

[7] 7.Banaś, J., Compactness conditions in the geometric theory of Banach spaces, Nonlinear Anal. 16 (1991), 669–682. Google Scholar | DOI

[8] 8.Banaś, J. and Fraczek, K., Locally nearly uniformly smooth Banach spaces, Collect. Math. 44 (1993), 13–22. Google Scholar

[9] 9.Banaś, J. and Fraczek, K., Conditions involving compactness in geometry of Banach spaces, Nonlinear Anal. 20 (1993), 1217–1230. Google Scholar | DOI

[10] 10.Banaś, J. and Goebel, K., Measure of noncompactness in Banach spaces, Lecture Notes in Pure and Appl. Math. 60 (Marcel Dekker, 1980). Google Scholar

[11] 11.Partington, J. R., On nearly uniformly convex Banach spaces, Math. Proc. Cambridge Philos. Soc. 93 (1983), 127–129. Google Scholar | DOI

[12] 12.Leonard, I. E., Banach sequence spaces, J. Math. Anal. Appl. 54 (1976), 245–265. Google Scholar | DOI

Cité par Sources :