Functional Space C (ω), C 0 (ω)

Katuhiko Kanazashi; Hiroyuki Okazaki; Yasunari Shidama

Formalized Mathematics (2012)

  • Volume: 20, Issue: 1, page 15-22
  • ISSN: 1426-2630

Abstract

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In this article, first we give a definition of a functional space which is constructed from all complex-valued 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 complex-valued continuous functions with bounded support. We also prove that this function space is a complex normed space.

How to cite

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Katuhiko Kanazashi, Hiroyuki Okazaki, and Yasunari Shidama. " Functional Space C (ω), C 0 (ω) ." Formalized Mathematics 20.1 (2012): 15-22. <http://eudml.org/doc/268270>.

@article{KatuhikoKanazashi2012,
abstract = {In this article, first we give a definition of a functional space which is constructed from all complex-valued 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 complex-valued continuous functions with bounded support. We also prove that this function space is a complex normed space.},
author = {Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {15-22},
title = { Functional Space C (ω), C 0 (ω) },
url = {http://eudml.org/doc/268270},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Katuhiko Kanazashi
AU - Hiroyuki Okazaki
AU - Yasunari Shidama
TI - Functional Space C (ω), C 0 (ω)
JO - Formalized Mathematics
PY - 2012
VL - 20
IS - 1
SP - 15
EP - 22
AB - In this article, first we give a definition of a functional space which is constructed from all complex-valued 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 complex-valued continuous functions with bounded support. We also prove that this function space is a complex normed space.
LA - eng
UR - http://eudml.org/doc/268270
ER -

References

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