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2012 | 20 | 1 | 15-22
Tytuł artykułu

Functional SpaceC(ω),C0(ω)

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Słowa kluczowe
Wydawca
Rocznik
Tom
20
Numer
1
Strony
15-22
Opis fizyczny
Daty
wydano
2012-01-01
online
2012-09-12
Twórcy
  • Shizuoka City, Japan
  • Shinshu University, Nagano, Japan
  • Shinshu University, Nagano, Japan
Bibliografia
  • Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
  • Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  • Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • Agata Darmochwał. Compact spaces. Formalized Mathematics, 1(2):383-386, 1990.
  • Noboru Endou. Banach algebra of bounded complex linear operators. Formalized Mathematics, 12(3):237-242, 2004.
  • Noboru Endou. Banach space of absolute summable complex sequences. Formalized Mathematics, 12(2):191-194, 2004.
  • Noboru Endou. Complex Banach space of bounded linear operators. Formalized Mathematics, 12(2):201-209, 2004.
  • Noboru Endou. Complex linear space and complex normed space. Formalized Mathematics, 12(2):93-102, 2004.
  • Noboru Endou. Complex linear space of complex sequences. Formalized Mathematics, 12(2):109-117, 2004.
  • Noboru Endou. Complex valued functions space. Formalized Mathematics, 12(3):231-235, 2004.
  • Noboru Endou. Continuous functions on real and complex normed linear spaces. Formalized Mathematics, 12(3):403-419, 2004.
  • Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
  • Katuhiko Kanazashi, Hiroyuki Okazaki, and Yasunari Shidama. Banach algebra of bounded complex-valued functionals. Formalized Mathematics, 19(2):121-126, 2011, doi: 10.2478/v10037-011-0019-0.[Crossref]
  • Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
  • Chanapat Pacharapokin, Hiroshi Yamazaki, Yasunari Shidama, and Yatsuka Nakamura. Complex function differentiability. Formalized Mathematics, 17(2):67-72, 2009, doi: 10.2478/v10037-009-0007-9.[Crossref]
  • Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • 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.[Crossref]
  • Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  • Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
  • Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-012-0003-3
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