Advances in Operator Theory
- Adv. Oper. Theory
- Volume 3, Number 4 (2018), 794-806.
A Banach algebra with its applications over paths of bounded variation
Let $C[0,T]$ denote the space of continuous real-valued functions on $[0,T]$. In this paper we introduce two Banach algebras: one of them is defined on $C[0,T]$ and the other is a space of equivalence classes of measures over paths of bounded variation on $[0,T]$. We establish an isometric isomorphism between them and evaluate analytic Feynman integrals of the functions in the Banach algebras, which play significant roles in the Feynman integration theories and quantum mechanics.
Adv. Oper. Theory, Volume 3, Number 4 (2018), 794-806.
Received: 11 February 2018
Accepted: 14 May 2018
First available in Project Euclid: 8 June 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]
Secondary: 28C20 60H05
Cho, Dong Hyun. A Banach algebra with its applications over paths of bounded variation. Adv. Oper. Theory 3 (2018), no. 4, 794--806. doi:10.15352/aot.1802-1310. https://projecteuclid.org/euclid.aot/1528444823