Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

An averaging property of the range of a vector measure


Authors: J. Diestel and C. J. Seifert
Journal: Bull. Amer. Math. Soc. 82 (1976), 907-909
MSC (1970): Primary 28A45
DOI: https://doi.org/10.1090/S0002-9904-1976-14207-3
MathSciNet review: 0419722
Full-text PDF

References | Similar Articles | Additional Information

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 48 #11436. MR 333111
  • 2. S. Banach, Théorie des operationes linéaires, Warzawa, 1932.
  • 3. R. G. Bartle, N. Dunford and J. T. Schwartz, Weak compactness and vector measures, Canad. J. Math. 7 (1955), 289-305. MR 16, 1123. MR 70050
  • 4. E. D. Bolker, A class of convex bodies, Trans. Amer. Math. Soc. 145 (1969), 323-345. MR 41 #921. MR 256265
  • 5. J. Bretagnolle, D. Dacunha-Castelle and J. L. Krivine, Lois stables et espaces L, Ann. Inst. Poincaré Sect. B (N. S. ) 2 (1965/66), 231-259. MR 34 #3605. MR 203757
  • 6. J. Diestel, Geometry of Banach spaces: Selected topics, Lecture Notes in Math., no. 485, Springer-Verlag, 1975. MR 461094
  • 7. L. Dor, Potentials and isometric embeddings in L (preprint).
  • 8. S. Kaczmarz and H. Steinhaus, Theorie der Orthogonalreihen, Warzawa, 1935.
  • 9. S. Kakutani, Concrete representation of abstract (M)-spaces. (A characterization of the space of continuous functions), Ann. of Math. (2) 42 (1941), 994-1024. MR 3, 205. MR 5778
  • 10. I. Kluvanek, A measure whose range contains a ball in l, Notices Amer. Math. Soc. 21 (1974), A-S39. Abstract 74T-B206.
  • 11. I. Kluvanek, The closed convex hull of the range of a vector measure (preprint).
  • 12. I. Kluvanek and G. Knowles, Vector measures and optimal controls (manuscript).
  • 13. A. Liapounoff, Sur les fonctions-vecteurs complètement additives, Izv. Akad. Nauk SSSR Ser. Mat. 4 (1940), 465-478. MR 2, 315. MR 4080
  • 14. J. Lindenstrauss, A short proof of Liapounoff's convexity theorem, J. Math. Mech. 15 (1966), 971-972. MR 34 #7754. MR 207941
  • 15. J. Lindenstrauss and A. Peχczyński, Absolutely summing operators in L, Studia Math. 29 (1968), 275-326. MR 37 #6743. MR 231188
  • 16. W. Szlenk, Sur les suites faiblement convergentes dans l'espace L, Studia Math. 25 (1965), 337-341. MR 34 #1833. MR 201956

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 28A45

Retrieve articles in all journals with MSC (1970): 28A45


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1976-14207-3

American Mathematical Society