Continuity of random derivations

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

doi:10.1090/S0002-9939-1995-1217455-3

Continuity of random derivations
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by M. V. Velasco and A. R. Villena PDF

Proc. Amer. Math. Soc. 123 (1995), 107-120 Request permission

Abstract:

In this paper we extend the well-known Johnson-Sinclair theorem in a stochastic sense showing that stochastically derivative linear random operators on semisimple Banach algebras are stochastically continuous. Besides, we prove that probably derivative linear random operators on semisimple Banach algebras are probably continuous.

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