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Geometric properties of Köthe–Bochner spaces

Published online by Cambridge University Press:  24 October 2008

Joan Cerdà
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, E-08071 Barcelona, Spain, e-mail: [email protected]
Henryk Hudzik
Affiliation:
Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/59, 60-769 Poznań, Poland, e-mail: [email protected], [email protected]
Mieczysław Mastyło
Affiliation:
Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/59, 60-769 Poznań, Poland, e-mail: [email protected], [email protected]

Abstract

Convexity, monotonicity and smoothness properties of Köthe spaces of vector-valued functions are described.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

[AS]Akcoglu, M. A. and Sucheston, L.. On uniform monotonicity of norms and ergodic theorems in function spaces. Re. Circ. Mat. Palermo (2), Suppl. 8 (1985), 325335.Google Scholar
[Bi]Birkhoff, G.. Lattice theory (Amer. Math. Soc., 1967).Google Scholar
[BH]Bru, B. and Heinich, H.. Applications de la dualité dans les espaces de Köthe. Studia Math. 93 (1989), 4169.CrossRefGoogle Scholar
[Bu]Bukhvalov, A. V.. On an analytic representation of operators with abstract norm. Izv. Vyss. Uceb. Zaved. 11 (1975), 2132.Google Scholar
[CHM]Cerdà, J., Hudzik, H. and Mastylo, M.. On the geometry of some Calderón Lozanovskii spaces. Indag. Mathem. 6 (1995), 3549.Google Scholar
[CP1]Castaing, Ch. and Pluciennik, R.. Denting points in Kothe-Bochner spaces. Set-valued Analysis 2 (1994), 439458.CrossRefGoogle Scholar
[CP2]Castaing, Ch. and Pluciennik, R.. Property (H) in Köthe-Bochner spaces. C.R. Acad. Sci. Paris, t. 319, Serie I (1994), 11591163.Google Scholar
[Da]Day, M. M., Some more uniformly convex spaces. Proc. Amer. Math. Soc. 47 (1941), 504507.Google Scholar
[DK]Deeb, W. and Khalil, R.. Smooth points of vector valued function spaces. Rocky Mtn. J. Math. 24 (1993), 505512.Google Scholar
[EV]Emmanuele, G. and Vilani, A.. Lifting of rotundity properties from E to L p(μ, E). Rocky Mtn. J. Math. 17 (1987), 617629.CrossRefGoogle Scholar
[Grl]Greim, P.. An extremal vector-valued L p-function taking no extremal vector as values. Proc. Amer. Math. Soc. 84 (1982), 6568.Google Scholar
[Gr2]Greim, P.. Strongly exposed points in Bochner L p spaces. Proc. Amer. Math. Soc. 88 (1983), 8184.Google Scholar
[Gr3]Greim, P.. A note on strong extreme and strongly exposed points in Bochner L p spaces. Proc. Amer. Math. Soc. 84 (1985), 6566.Google Scholar
[Ha]Halperin, I.. Uniform convexity in function spaces. Duke Math. J. 21 (1954), 195204.CrossRefGoogle Scholar
[HL1]Hu, Z. and Lin, B. L.. RNP and CPCP Lebesgue Bochner function spaces. Illinois J. Math. 37 (1993), 329347.Google Scholar
[HL2]Hu, Z. and Lin, B. L.. Strongly exposed points in Lebesgue-Bochner function spaces. Proc. Amer. Math. Soc. 120 (1994), 11591165.Google Scholar
[HK]Hudzik, H. and Kurc, W.. Monotonicity properties of Musielak-Orlicz spaces and dominated best approximation in Banach lattices, preprint.Google Scholar
[HL]Hudzik, H. and Landes, T.. Characteristic of convexity of Kothe-Bochner spaces. Math. Ann. 294 (1992), 117124.Google Scholar
[HM1]Hudzik, H. and Mastylo, M.. Strongly extreme points in Kothe-Bochner spaces. Rocky Mtn. J. Math. 23 (1993), 899909.CrossRefGoogle Scholar
[HM2]Hudzik, H. and Mastylo, M.. Local uniform rotundity in Banach spaces via sublinear operators, to appear in Math. Japonica.Google Scholar
[Jo]Johnson, J.. Strongly exposed points in L p(μ, X). Rocky Mtn. J. Math. 10 (1980), 517519.CrossRefGoogle Scholar
[Ka]Kaminska, A.. Some convexity properties of Musielak-Orlicz spaces of Bochner type, in Proc. 13th Winter School on Abstract Analysis, Srni, 2027 January 1995, Supl. Rendiconti Circolo Math. Palermo. Serie II, 10 (1995), 6373.Google Scholar
[KT]Kaminska, A. and Turett, B.. Rotundity in Kothe spaces of vector-valued functions. Canadian J. Math. 41 (1989), 659675.Google Scholar
[KA]Kantorovitch, L. and Akilov, G.. Functional analysis, 2nd ed., in Russian (MIR, 1972).Google Scholar
[KR]Kuratowski, K. and Ryll-Xardzewski, C.. A general theorem on selectors. Bull. Acacl. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 397403.Google Scholar
[Kul]Kurc, W.. Strongly exposed points in Orlicz spaces of vector-valued functions, I. Comment. Math. (Prace Mat.) 27 (1987), 121134.Google Scholar
[Ku2]Kurc, W.. Strictly and uniformly monotone Musielak-Orlicz spaces and applications to best approximation. J. Approx. Theory (2) 69 (1992), 173187.Google Scholar
[LL1]Lin, B. L. and Lin, P. K.. Denting points in Bochner Lp-spsices. Proc. Amer. Math. Soc. 97 (1986), 629633.Google Scholar
[LL2]Lin, B. L. and Lin, P. K.. Property (H) in Lebesgue-Bochner function spaces. Proc. Amer. Math. Soc. 95 (1985), 581584.Google Scholar
[LT]Lindenstrauss, J. and Tzafriri, L.. Classical Banach spaces II (Springer-Verlag, 1979).CrossRefGoogle Scholar
[Sm]Smith, M.. Strongly extreme points in L p(μ, X). Rocky Mtn. J. Math. 16 (1986), 15.CrossRefGoogle Scholar
[Su]Sundaresan, K.. Extreme points of the unit cell in Lebesgue-Bochner function spaces. Colloquium Math. 22 (1970), 111119.Google Scholar