# 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

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topKatuhiko 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 -

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