Topological algebras of random elements
Volume 233 / 2016
Studia Mathematica 233 (2016), 101-117
MSC: Primary 46H05, 46H10, 46H25, 46H40; Secondary 60B05, 60B11.
DOI: 10.4064/sm7938-4-2016
Published online: 19 May 2016
Abstract
Let $L_0(\varOmega ;A)$ be the Fréchet space of Bochner-measurable random variables with values in a unital complex Banach algebra $A$. We study $L_0(\varOmega ;A)$ as a topological algebra, investigating the notion of spectrum in $L_0(\varOmega ;A)$, the Jacobson radical, ideals, hulls and kernels. Several results on automatic continuity of homomorphisms are developed, including versions of well-known theorems of C. Rickart and B. E. Johnson.
