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

Katuhiko Kanazashi; Noboru Endou; Yasunari Shidama

doi:10.2478/v10037-010-0002-1

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

Formalized Mathematics

Volume 18 (2010): Issue 1 (March 2010)

By: Katuhiko Kanazashi, Noboru Endou and Yasunari Shidama

Open Access

|Jan 2011

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.

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Articles in this issue

DOI: https://doi.org/10.2478/v10037-010-0002-1 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 11 - 16

Published on: Jan 5, 2011

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Related subjects:

Mathematics,

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2011 Katuhiko Kanazashi, Noboru Endou, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 18 (2010): Issue 1 (March 2010)