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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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ISSN
1898-9934
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Volume 18, Issue 1 (Jan 2010)

Issues

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

Katuhiko Kanazashi
  • Shizuoka High School, Japan
/ Noboru Endou
  • Gifu National College of Technology, Japan
/ Yasunari Shidama
  • Shinshu University, Nagano, Japan
Published Online: 2011-01-05 | DOI: https://doi.org/10.2478/v10037-010-0002-1

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

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.

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About the article


Published Online: 2011-01-05

Published in Print: 2010-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-010-0002-1. Export Citation

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