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)

 
 

 

A random Banach-Steinhaus theorem


Authors: M. V. Velasco and A. R. Villena
Journal: Proc. Amer. Math. Soc. 123 (1995), 2489-2497
MSC: Primary 60H25; Secondary 47B80, 60B11
DOI: https://doi.org/10.1090/S0002-9939-1995-1254856-1
MathSciNet review: 1254856
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In an earlier paper, we began a study of linear random operators which have a certain probability of behaving as continuous operators. In this paper we study the pointwise limit in probability of a sequence of such operators, extending the Banach-Steinhaus theorem in a stochastical sense.


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

  • [1] A. T. Bharucha-Reid, Random integral equations, Academic Press, New York and London, 1972. MR 0443086 (56:1459)
  • [2] M. Ledoux and M. Talagrand, Probability in Banach spaces, Springer-Verlag, New York, 1991. MR 1102015 (93c:60001)
  • [3] A. V. Skorohod, Random linear operators, Reidel, Holland, 1984. MR 733994 (85a:60070)
  • [4] M. V. Velasco and A. R. Villena, Continuity of random derivations, Proc. Amer. Math. Soc. 123 (1995), 107-120. MR 1217455 (95c:46073)
  • [5] -, A random closed graph theorem (submitted).
  • [6] A. R. Villena, Stochastic continuity of random derivations on $ {H^ \ast }$-algebras, Proc. Amer. Math. Soc. 123 (1995), 785-796. MR 1223522 (95d:46049)
  • [7] A. Wilansky, Modern methods in topological vector spaces, McGraw-Hill, New York, 1978. MR 518316 (81d:46001)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60H25, 47B80, 60B11

Retrieve articles in all journals with MSC: 60H25, 47B80, 60B11


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1254856-1
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society