Pacific Journal of Mathematics

An analogue of Liapounoff's convexity theorem for Birnbaum-Orlicz spaces and the extreme points of their unit balls.

I. Glicksberg

Article information

Source
Pacific J. Math., Volume 116, Number 2 (1985), 265-283.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102707064

Mathematical Reviews number (MathSciNet)
MR771636

Zentralblatt MATH identifier
0581.46020

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Citation

Glicksberg, I. An analogue of Liapounoff's convexity theorem for Birnbaum-Orlicz spaces and the extreme points of their unit balls. Pacific J. Math. 116 (1985), no. 2, 265--283. https://projecteuclid.org/euclid.pjm/1102707064


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References

  • [1] Z. Birnbaum and W. Orlicz, Uber die Veralgemeinerungdes Begriffes derzueinander konjugiertan Potentzen, Studia Math.,3 (1931), 1-67.
  • [2] I. Glicksberg, A controlledapproach to Liapounoff9s convexity theorem, J. Math. Anal. and Appl., 94 (1983), 193-196.
  • [3] M. A. Kransnoselsk and Y. B. Rutickii, Convex Functions and Orlicz Spaces, P. Noordhoff Ltd, Groningen,1961.
  • [4] A. Liapounoff, Sur les fonctions-vecteurs completement additives, Bull. Acad. Sci. URSS, 4 (1940), 465-478.
  • [5] J. Lindenstrauss, A shortproof of Liapounoff's convexity theorem, J. Math. Mech., 15 (1966), 971-2.
  • [6] W. Rudin, Functional Analysis, McGraw Hill, N.Y., 1973.
  • [7] A. Zygmund, Trigonometric Series, 2nd ed., Cambridge Univ. Press, 1958.