Characterization of strongly exposed points in general Kothe-Bochner Banach spaces

• Autorzy: Benabdellah H. , Lalaoui Rhali M. H.
• Języki publikacji: EN

Abstrakty

EN

We study strongly exposed points in general Kothe-Bochner Banach spaces X(E). We first give a characterization of strongly exposed points of the set of X-selections of a measurable multifunction [Gamma]. We then apply this result to the study of strongly exposed points of the closed unit ball of X(E). Precisely we show that if an element f is a strongly exposed point of B_X(E), then |f| is a strongly exposed point of B_x and f(omega)/||f(omega)[| is a strongly exposed point of B_E for [my]-almost all [omega is an element of S(f)].

Słowa kluczowe

EN

Kothe-Bochner Banach spaces; strongly extreme points; measurable selections

PL

przestrzeń Kothe-Bochnera Banacha; punkt silnie ekstremalny; wybór mierzalny

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 1
• Strony: 9--18
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Benabdellah H.

• Department of Mathematics, University Cadi Ayyad, Faculty of Sciences Semlalia, P.O. Box 2390, Marrakesh, Morocco

autor

Lalaoui Rhali M. H.

• Department of Mathematics, University Cadi Ayyad, Faculty of Sciences Semlalia, P.O. Box 2390, Marrakesh, Morocco

Bibliografia

• [1] H. Benabdellah, Contribution aux problèmes de convergence fort-faible, à la géométrie des espaces de Banach et aux inclusions différentielles, doctoral thesis, Univ. Montpellier II, 1991.
• [2] -, Denting points in Bochner Banach ideal spaces X (E), J. Convex Anal. 6 (1999), 183-194.
• [3] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, Berlin, 1977.
• [4] P. Greim, Strongly exposed points in Bochner Lp-spaces, Proc. Amer. Math. Soc. 88 (1983), 81-84.
• [5] -, A note on strongly extreme and strongly exposed points in Bochner Lp-spaces, ibid. 93 (1985), 65-66.
• [6] R. Grząślewicz, H. Hudzik and W. Kurc, Extreme and exposed points in Orlicz spaces, Canad. J. Math. 44 (1992), 505-515.
• [7] C. J. Himmelberg, Measurable relations, Fund. Math. 87 (1975), 53-72.
• [8] Z. B. Hu and B. L. Lin, Strongly exposed points in Lebesgue Bochner function spaces, Proc. Amer. Math. Soc. 120 (1994), 1159-1165.
• [9] -, -, Extremal structure of the unit ball of Lp(μ;X)*, J. Math. Anal. Appl. 200 (1996), 567-590.
• [10] B. L. Lin and P. K. Lin, Denting points in Bochner Lp-spaces, Proc. Amer. Math. Soc. 97 (1986), 629-633.
• [11] B. L. Lin, P. K. Lin and S. L. Troyanski, Characterizations of denting points, ibid. 102 (1988), 526-528.
• [12] P. K. Lin and H. Y. Sun, Denting points in Köthe-Bochner function spaces, preprint.
• [13] P. K. Lin and H. Y. Sun, Extremity in Köthe-Bochner function spaces, J. Math. Anal. Appl. 218 (1998), 136-154.
• [14] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II. Function Spaces, Ergeb. Math. Grenzgeb. 97, Springer, New York, 1979.
• [15] M. Talagrand, Weak Cauchy sequences in L1(E), Amer. J. Math. 106 (1984), 703-724.