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.

**[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*-*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)**

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