Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T07:40:33.575Z Has data issue: false hasContentIssue false
  • English
  • Français

Geometric properties of Köthe–Bochner spaces

Published online by Cambridge University Press:  24 October 2008

Joan Cerdà ,
Henryk Hudzik  and
Mieczysław Mastyło
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]
Get access Rights & Permissions [Opens in a new window]

Abstract

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

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 3 , October 1996 , pp. 521 - 533
Copyright
Copyright © Cambridge Philosophical Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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), 325–335.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), 41–69.CrossRefGoogle Scholar
[Bu]Bukhvalov, A. V.. On an analytic representation of operators with abstract norm. Izv. Vyss. Uceb. Zaved. 11 (1975), 21–32.Google Scholar
[CHM]Cerdà, J., Hudzik, H. and Mastylo, M.. On the geometry of some Calderón Lozanovskii spaces. Indag. Mathem. 6 (1995), 35–49.Google Scholar
[CP1]Castaing, Ch. and Pluciennik, R.. Denting points in Kothe-Bochner spaces. Set-valued Analysis 2 (1994), 439–458.CrossRefGoogle Scholar
[CP2]Castaing, Ch. and Pluciennik, R.. Property (H) in Köthe-Bochner spaces. C.R. Acad. Sci. Paris, t. 319, Serie I (1994), 1159–1163.Google Scholar
[Da]Day, M. M., Some more uniformly convex spaces. Proc. Amer. Math. Soc. 47 (1941), 504–507.Google Scholar
[DK]Deeb, W. and Khalil, R.. Smooth points of vector valued function spaces. Rocky Mtn. J. Math. 24 (1993), 505–512.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), 617–629.CrossRefGoogle Scholar
[Grl]Greim, P.. An extremal vector-valued L p-function taking no extremal vector as values. Proc. Amer. Math. Soc. 84 (1982), 65–68.Google Scholar
[Gr2]Greim, P.. Strongly exposed points in Bochner L p spaces. Proc. Amer. Math. Soc. 88 (1983), 81–84.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), 65–66.Google Scholar
[Ha]Halperin, I.. Uniform convexity in function spaces. Duke Math. J. 21 (1954), 195–204.CrossRefGoogle Scholar
[HL1]Hu, Z. and Lin, B. L.. RNP and CPCP Lebesgue Bochner function spaces. Illinois J. Math. 37 (1993), 329–347.Google Scholar
[HL2]Hu, Z. and Lin, B. L.. Strongly exposed points in Lebesgue-Bochner function spaces. Proc. Amer. Math. Soc. 120 (1994), 1159–1165.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), 117–124.Google Scholar
[HM1]Hudzik, H. and Mastylo, M.. Strongly extreme points in Kothe-Bochner spaces. Rocky Mtn. J. Math. 23 (1993), 899–909.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), 517–519.CrossRefGoogle Scholar
[Ka]Kaminska, A.. Some convexity properties of Musielak-Orlicz spaces of Bochner type, in Proc. 13th Winter School on Abstract Analysis, Srni, 20–27 January 1995, Supl. Rendiconti Circolo Math. Palermo. Serie II, 10 (1995), 63–73.Google Scholar
[KT]Kaminska, A. and Turett, B.. Rotundity in Kothe spaces of vector-valued functions. Canadian J. Math. 41 (1989), 659–675.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), 397–403.Google Scholar
[Kul]Kurc, W.. Strongly exposed points in Orlicz spaces of vector-valued functions, I. Comment. Math. (Prace Mat.) 27 (1987), 121–134.Google Scholar
[Ku2]Kurc, W.. Strictly and uniformly monotone Musielak-Orlicz spaces and applications to best approximation. J. Approx. Theory (2) 69 (1992), 173–187.Google Scholar
[LL1]Lin, B. L. and Lin, P. K.. Denting points in Bochner Lp-spsices. Proc. Amer. Math. Soc. 97 (1986), 629–633.Google Scholar
[LL2]Lin, B. L. and Lin, P. K.. Property (H) in Lebesgue-Bochner function spaces. Proc. Amer. Math. Soc. 95 (1985), 581–584.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), 1–5.CrossRefGoogle Scholar
[Su]Sundaresan, K.. Extreme points of the unit cell in Lebesgue-Bochner function spaces. Colloquium Math. 22 (1970), 111–119.Google Scholar