Displaying similar documents to “Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support”

Functional Space C (ω), C 0 (ω)

Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama (2012)

Formalized Mathematics

Similarity:

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.

Banach Algebra of Bounded Functionals

Yasunari Shidama, Hikofumi Suzuki, Noboru Endou (2008)

Formalized Mathematics

Similarity:

In this article, we describe some basic properties of the Banach algebra which is constructed from all bounded functionals.MML identifier: C0SP1, version: 7.8.10 4.99.1005

Dual Spaces and Hahn-Banach Theorem

Keiko Narita, Noboru Endou, Yasunari Shidama (2014)

Formalized Mathematics

Similarity:

In this article, we deal with dual spaces and the Hahn-Banach Theorem. At the first, we defined dual spaces of real linear spaces and proved related basic properties. Next, we defined dual spaces of real normed spaces. We formed the definitions based on dual spaces of real linear spaces. In addition, we proved properties of the norm about elements of dual spaces. For the proof we referred to descriptions in the article [21]. Finally, applying theorems of the second section, we proved...

Cartesian Products of Family of Real Linear Spaces

Hiroyuki Okazaki, Noboru Endou, Yasunari Shidama (2011)

Formalized Mathematics

Similarity:

In this article we introduced the isomorphism mapping between cartesian products of family of linear spaces [4]. Those products had been formalized by two different ways, i.e., the way using the functor [:X, Y:] and ones using the functor "product". By the same way, the isomorphism mapping was defined between Cartesian products of family of linear normed spaces also.

Banach Algebra of Bounded Complex-Valued Functionals

Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama (2011)

Formalized Mathematics

Similarity:

In this article, we describe some basic properties of the Banach algebra which is constructed from all bounded complex-valued functionals.

Contracting Mapping on Normed Linear Space

Keiichi Miyajima, Artur Korniłowicz, Yasunari Shidama (2012)

Formalized Mathematics

Similarity:

In this article, we described the contracting mapping on normed linear space. Furthermore, we applied that mapping to ordinary differential equations on real normed space. Our method is based on the one presented by Schwarz [29].

On L 1 Space Formed by Complex-Valued Partial Functions

Yasushige Watase, Noboru Endou, Yasunari Shidama (2012)

Formalized Mathematics

Similarity:

In this article, we formalized L1 space formed by complexvalued partial functions [11], [15]. The real-valued case was formalized in [22] and this article is its generalization.