A random Banach-Steinhaus theorem

Velasco, M. V.; Villena, A. R.

doi:10.1090/S0002-9939-1995-1254856-1

A random Banach-Steinhaus theorem
HTML articles powered by AMS MathViewer

by M. V. Velasco and A. R. Villena PDF

Proc. Amer. Math. Soc. 123 (1995), 2489-2497 Request permission

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

A. T. Bharucha-Reid, Random integral equations, Mathematics in Science and Engineering, Vol. 96, Academic Press, New York-London, 1972. MR 0443086
Michel Ledoux and Michel Talagrand, Probability in Banach spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 23, Springer-Verlag, Berlin, 1991. Isoperimetry and processes. MR 1102015, DOI 10.1007/978-3-642-20212-4
A. V. Skorohod, Random linear operators, Mathematics and its Applications (Soviet Series), D. Reidel Publishing Co., Dordrecht, 1984. Translated from the Russian. MR 733994, DOI 10.1007/978-94-009-6063-3
M. V. Velasco and A. R. Villena, Continuity of random derivations, Proc. Amer. Math. Soc. 123 (1995), no. 1, 107–120. MR 1217455, DOI 10.1090/S0002-9939-1995-1217455-3

A random closed graph theorem

A. R. Villena, Stochastic continuity of random derivations on $H^*$-algebras, Proc. Amer. Math. Soc. 123 (1995), no. 3, 785–796. MR 1223522, DOI 10.1090/S0002-9939-1995-1223522-0
Albert Wilansky, Modern methods in topological vector spaces, McGraw-Hill International Book Co., New York, 1978. MR 518316