A Banach Algebra Similar to Cameron-Storvick’s One with Its Equivalent Spaces

Abstract

Let C[0,T] denote an analogue of a generalized Wiener space, that is, the space of continuous, real-valued functions on the interval [0,T]. In this paper, we introduce a Banach algebra on C[0,T] which generalizes Cameron-Storvick’s one, the space of generalized Fourier-Stieltjes transforms of the C-valued, and finite Borel measures on L2[0,T]. We also investigate properties of the Banach algebra on C[0,T] and equivalence between the Banach algebra and the Fresnel class which plays a significant role in Feynman integration theories and quantum mechanics.