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2012 | 20 | 4 | 271-274
Tytuł artykułu

Banach’s Continuous Inverse Theorem and Closed Graph Theorem

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article we formalize one of the most important theorems of linear operator theory - the Closed Graph Theorem commonly used in a standard text book such as [10] in Chapter 24.3. It states that a surjective closed linear operator between Banach spaces is bounded.
Słowa kluczowe
Wydawca
Rocznik
Tom
20
Numer
4
Strony
271-274
Opis fizyczny
Daty
wydano
2012-12-01
online
2013-02-02
Twórcy
  • 406-3, Haneo, Naganohara Agatuma, Gunma, Japan
  • Shinshu University, Nagano, Japan
  • Shinshu University, Nagano, Japan
Bibliografia
  • [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [2] Czesław Bylinski. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.
  • [3] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [4] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [5] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [6] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [7] Czesław Bylinski. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005.
  • [8] Noboru Endou, Yasumasa Suzuki, and Yasunari Shidama. Real linear space of real sequences. Formalized Mathematics, 11(3):249-253, 2003.
  • [9] Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
  • [10] Isao Miyadera. Functional Analysis. Riko-Gaku-Sya, 1972.
  • [11] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.
  • [12] Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. Cartesian products of family of real linear spaces. Formalized Mathematics, 19(1):51-59, 2011, doi: 10.2478/v10037-011-0009-2.[Crossref]
  • [13] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • [14] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
  • [15] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.
  • [16] Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. FormalizedMathematics, 1(2):297-301, 1990.
  • [17] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [19] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [20] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-012-0032-y
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