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

Katuhiko Kanazashi; Noboru Endou; Yasunari Shidama

Formalized Mathematics (2010)

  • Volume: 18, Issue: 1, page 11-16
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Katuhiko Kanazashi, Noboru Endou, and Yasunari Shidama. "Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support." Formalized Mathematics 18.1 (2010): 11-16. <http://eudml.org/doc/267340>.

@article{KatuhikoKanazashi2010,
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.},
author = {Katuhiko Kanazashi, Noboru Endou, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {11-16},
title = {Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support},
url = {http://eudml.org/doc/267340},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Katuhiko Kanazashi
AU - Noboru Endou
AU - Yasunari Shidama
TI - Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support
JO - Formalized Mathematics
PY - 2010
VL - 18
IS - 1
SP - 11
EP - 16
AB - 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.
LA - eng
UR - http://eudml.org/doc/267340
ER -

References

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