## Advances in Operator Theory

### A Banach algebra with its applications over paths of bounded variation

Dong Hyun Cho

#### Abstract

‎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.

#### Article information

Source
Adv. Oper. Theory, Volume 3, Number 4 (2018), 794-806.

Dates
Received: 11 February 2018
Accepted: 14 May 2018
First available in Project Euclid: 8 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.aot/1528444823

Digital Object Identifier
doi:10.15352/aot.1802-1310

Mathematical Reviews number (MathSciNet)
MR3856173

Zentralblatt MATH identifier
06946378

Subjects
Primary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]
Secondary: 28C20‎ ‎60H05

#### Citation

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

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