Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support

Open access

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.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics 1(1):91-96 1990.

  • [2] Czesław Byliński. Binary operations. Formalized Mathematics 1(1):175-180 1990.

  • [3] Czesław Byliński. Functions from a set to a set. Formalized Mathematics 1(1):153-164 1990.

  • [4] Czesław Byliński. Partial functions. Formalized Mathematics 1(2):357-367 1990.

  • [5] Czesław Byliński. Some basic properties of sets. Formalized Mathematics 1(1):47-53 1990.

  • [6] Czesław Byliński and Piotr Rudnicki. Bounding boxes for compact sets in ε2. Formalized Mathematics 6(3):427-440 1997.

  • [7] Agata Darmochwał. Compact spaces. Formalized Mathematics 1(2):383-386 1990.

  • [8] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics 1(1):35-40 1990.

  • [9] Eugeniusz Kusak Wojciech Leończuk and Michał Muzalewski. Abelian groups fields and vector spaces. Formalized Mathematics 1(2):335-342 1990.

  • [10] Henryk Oryszczyszyn and Krzysztof Prażmowski. Real functions spaces. Formalized Mathematics 1(3):555-561 1990.

  • [11] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics 1(1):223-230 1990.

  • [12] Jan Popiołek. Real normed space. Formalized Mathematics 2(1):111-115 1991.

  • [13] Yasunari Shidama. The Banach algebra of bounded linear operators. Formalized Mathematics 12(2):103-108 2004.

  • [14] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics 12(1):39-48 2004.

  • [15] Yasunari Shidama Hikofumi Suzuki and Noboru Endou. Banach algebra of bounded functionals. Formalized Mathematics 16(2):115-122 2008 doi:10.2478/v10037-008-0017-z.

  • [16] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics 1(2):329-334 1990.

  • [17] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics 1(1):115-122 1990.

  • [18] Wojciech A. Trybulec. Groups. Formalized Mathematics 1(5):821-827 1990.

  • [19] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics 1(2):291-296 1990.

  • [20] Zinaida Trybulec. Properties of subsets. Formalized Mathematics 1(1):67-71 1990.

Search
Journal information
Impact Factor


CiteScore 2018: 0.42

SCImago Journal Rank (SJR) 2018: 0.111
Source Normalized Impact per Paper (SNIP) 2018: 0.169

Target audience:

researchers in the fields of formal methods and computer-checked mathematics

Cited By
Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 108 34 0
PDF Downloads 47 26 1