Let L₀(Ω;A) be the Fréchet space of Bochner-measurable random variables with values in a unital complex Banach algebra A. We study L₀(Ω;A) as a topological algebra, investigating the notion of spectrum in L₀(Ω;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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm7938-4-2016,
author = {Bertram M. Schreiber and M. Victoria Velasco},
title = {Topological algebras of random elements},
journal = {Studia Mathematica},
volume = {233},
year = {2016},
pages = {101-117},
zbl = {06586870},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm7938-4-2016}
}
Bertram M. Schreiber; M. Victoria Velasco. Topological algebras of random elements. Studia Mathematica, Tome 233 (2016) pp. 101-117. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm7938-4-2016/