<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>In this article, we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all real-valued continuous functions with bounded support. We prove that this function space is a real normed space.</p></abstract>

In this article, we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all real-valued continuous functions with bounded support. We prove that this function space is a real normed space.

Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support

Gifu National College of Technology, Japan

Formalized Mathematics

In this article, we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space. We prove...

Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support

Published Online: Jan 05, 2011

Page range: 11 - 16

DOI: https://doi.org/10.2478/v10037-010-0002-1

This content is open access.