Countably-Normed Spaces, Their Dual, and the Gaussian Measure

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Here we present an overview of countably-normed spaces. We discuss the main topologies--weak, strong, and inductive--placed on the dual of a countably-normed space and discuss the sigma-fields generated by these topologies. In particular, we show that under certain conditions the strong and inductive topologies coincide and the sigma-fields generated by the weak, strong, and inductive topologies are equal. With these sigma-fields, we develop a Gaussian measure on the dual of a nuclear space. The purpose in mind is to provide the background material for many of the results used is White Noise Analysis.
25 pages, 0 figures, Background material for White Noise Analysis

Keywords

Functional Analysis, 46A11

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/71861

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0407200
 http://arxiv.org/abs/math/0407200

Collections

arXiv