Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The range of a vector measure has the Banach-Saks property


Author: R. Anantharaman
Journal: Proc. Amer. Math. Soc. 66 (1977), 183-184
MSC: Primary 28A45
DOI: https://doi.org/10.1090/S0002-9939-1977-0480931-4
Addendum: Proc. Amer. Math. Soc. 71 (1978), 359.
MathSciNet review: 0480931
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The above result of Diestel and Seifert is proved using the Banach-Saks theorem for $ {L^p}(\lambda ),1 < p < \infty $.


References [Enhancements On Off] (What's this?)

  • [1] R. Anantharaman, On exposed points of the range of a vector measure, Vector and Operator Valued Measures and Applications (Proc. Sympos. Snowbird Resort, Alta, Utah, 1972), Academic Press, New York, 1973, pp. 7-22. MR 0333111 (48:11436)
  • [2] S. Banach and S. Saks, Sur la convergence forte dans les champs $ {L^p}$, Studia Math. 2 (1930), 51-57.
  • [3] R. G. Bartle, N. Dunford and J. T. Schwartz, Weak compactness and vector measures, Canad. J. Math. 7 (1955), 289-305. MR 0070050 (16:1123c)
  • [4] J. Diestel, Geometry of Banach spaces-Selected topics, Springer-Verlag, New York, 1975. MR 0461094 (57:1079)
  • [5] J. Diestel and C. J. Seifert, An averaging property of the range of a vector measure, Bull. Amer. Math. Soc. 82 (1976), 907-909. MR 0419722 (54:7740)
  • [6] W. Szlenk, Sur les suites faiblement convergentes dans l'espace L, Studia Math. 25 (1966), 337-341. MR 0201956 (34:1833)
  • [7] I. Tweddle, Weak compactness in locally convex spaces, Glasgow Math. J. 9 (1968), 123-127. MR 0239395 (39:752)
  • [8] -, Vector-valued measures, Proc. London Math. Soc. 20 (1970), 469-489. MR 0259065 (41:3707)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A45

Retrieve articles in all journals with MSC: 28A45


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0480931-4
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society