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Functional SpaceC(ω),C0(ω)

100%
Kanazashi K., Okazaki H., Shidama Y.
Formalized Mathematics
|
2012
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tom 20
|
nr 1
15-22
EN
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.
2
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Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support

100%
Kanazashi K., Endou N., Shidama Y.
Formalized Mathematics
|
2010
|
tom 18
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nr 1
11-16
EN
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.
3
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Banach Algebra of Bounded Complex-Valued Functionals

100%
Kanazashi K., Okazaki H., Shidama Y.
Formalized Mathematics
|
2011
|
tom 19
|
nr 2
121-126
EN
In this article, we describe some basic properties of the Banach algebra which is constructed from all bounded complex-valued functionals.
4
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The CkSpace

100%
Kanazashi K., Okazaki H., Shidama Y.
Formalized Mathematics
|
2013
|
tom 21
|
nr 1
25-31
EN
In this article, we formalize continuous differentiability of realvalued functions on n-dimensional real normed linear spaces. Next, we give a definition of the Ck space according to [23].
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