Topological algebras of random elements

Bertram M. Schreiber, and M. Victoria Velasco. "Topological algebras of random elements." Studia Mathematica 233.2 (2016): 101-117. <http://eudml.org/doc/285540>.

@article{BertramM2016,
abstract = {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.},
author = {Bertram M. Schreiber, M. Victoria Velasco},
journal = {Studia Mathematica},
keywords = {Banach algebra; topological algebra; F-algebra; spectrum; random element; radical; ideal; hull; kernel; homomorphism; automatic continuity},
language = {eng},
number = {2},
pages = {101-117},
title = {Topological algebras of random elements},
url = {http://eudml.org/doc/285540},
volume = {233},
year = {2016},
}

TY - JOUR
AU - Bertram M. Schreiber
AU - M. Victoria Velasco
TI - Topological algebras of random elements
JO - Studia Mathematica
PY - 2016
VL - 233
IS - 2
SP - 101
EP - 117
AB - 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.
LA - eng
KW - Banach algebra; topological algebra; F-algebra; spectrum; random element; radical; ideal; hull; kernel; homomorphism; automatic continuity
UR - http://eudml.org/doc/285540
ER -