Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3420181001A Banach algebra with its applications over paths of bounded variation7948066191010.15352/aot.1802-1310ENDong Hyun ChoDepartment of Mathematics, Kyonggi University, Suwon 16227, Republic of KoreaJournal Article20180211Let $C[0,T]$ 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.http://www.aot-math.org/article_61910_0e3e96a519a19ea5b64be80b3c07a269.pdf