## Keywords (9)

Publications
A new class of Banach spaces

# A new class of Banach spaces,10.1088/1751-8113/41/49/495206,Journal of Physics A-mathematical and Theoretical,T. L. Gill,W. W. Zachary

A new class of Banach spaces
In this paper, we construct a new class of separable Banach spaces {{\bb K}{\bb S}}^p , for 1 <= p <= ∞, each of which contains all of the standard Lp spaces, as well as the space of finitely additive measures, as compact dense embeddings. Equally important is the fact that these spaces contain all Henstock-Kurzweil integrable functions and, in particular, the Feynman kernel and the Dirac measure, as norm bounded elements. As a first application, we construct the elementary path integral in the manner originally intended by Feynman. We then suggest that {{\bb K}{\bb S}}^2 is a more appropriate Hilbert space for quantum theory, in that it satisfies the requirements for the Feynman, Heisenberg and Schrödinger representations, while the conventional choice only satisfies the requirements for the Heisenberg and Schrödinger representations. As a second application, we show that the mixed topology on the space of bounded continuous functions, {\mathbf{C}}_b [{\bb R}^n ] , used to define the weak generator for a semigroup T(t), is stronger than the norm topology on {{\bb K}{\bb S}}^p . (This means that, when extended to {{\bb K}{\bb S}}^p, T(t) is strongly continuous, so that the weak generator on {\mathbf{C}}_b [{\bb R}^n ] becomes a strong generator on {{\bb K}{\bb S}}^p .)
View Publication
 The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
 ( dx.doi.org ) ( stacks.iop.org ) ( adsabs.harvard.edu )

## References (11)

### On existence and nonexistence of proper(Citations: 7)

Published in 1975.

### Quantum Mechanics and Path Integrals(Citations: 2815)

Published in 1965.

### On natural adjoint operators in Banach Spaces(Citations: 3)

Published in 2004.

### Foundations for relativistic quantum theory. I. Feynman's operator calculus and the Dyson conjectures(Citations: 7)

Published in 2002.