The C k Space
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].
Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support
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.
Banach Algebra of Bounded Complex-Valued Functionals
In this article, we describe some basic properties of the Banach algebra which is constructed from all bounded complex-valued functionals.
Functional Space C (ω), C 0 (ω)
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.
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