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)

 
 

 

Extreme points in function spaces


Author: Dirk Werner
Journal: Proc. Amer. Math. Soc. 89 (1983), 598-600
MSC: Primary 46E40; Secondary 47D15
DOI: https://doi.org/10.1090/S0002-9939-1983-0718980-3
MathSciNet review: 718980
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the extreme points of the unit ball of $ C(K,{L^1}(\mu ))$ ($ K$ compact Hausdorff, $ (\Omega ,\Sigma ,\mu )$ arbitrary) are precisely the functions with extremal values. The result is applied to characterize the extreme points of the unit ball of certain spaces of compact operators.


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

  • [1] R. M. Blumenthal, J. Lindenstrauss and R. R. Phelps, Extreme operators into $ C(K)$, Pacific J. Math. 15 (1965), 747-756. MR 0209862 (35:758)
  • [2] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 0117523 (22:8302)
  • [3] P. Greim, An extremal vector-valued $ {L^p}$-function taking no extremal vectors as values, Proc. Amer. Math. Soc. 84 (1982), 65-68. MR 633279 (83c:46034)
  • [4] E. Michael, Continuous selections. I, Ann. of Math. (2) 63 (1956), 361-382. MR 0077107 (17:990e)
  • [5] P. D. Morris and R. R. Phelps, Theorems of Krein-Milman type for certain convex sets of operators, Trans. Amer. Math. Soc. 150 (1970), 183-200. MR 0262804 (41:7409)
  • [6] M. Sharir, Characterization and properties of extreme operators into $ C(Y)$, Israel J. Math. 12 (1972), 174-183. MR 0317026 (47:5574)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46E40, 47D15

Retrieve articles in all journals with MSC: 46E40, 47D15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0718980-3
Keywords: Extreme point, spaces of vector-valued functions, nice operator, spaces of compact operators
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society