## 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

#### 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

**Keywords**

Banach algebra Feynman integral Itô integral Paley-Wiener-Zygmund integral Wiener space

#### 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