Banach Algebra of Bounded Complex-Valued Functionals

• Autorzy: Katuhiko Kanazashi , Hiroyuki Okazaki , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2011
• Tom: 19
• Numer: 2
• Strony: 121-126

Daty

wydano

2011-01-01

online

2011-07-18

Twórcy

autor

Katuhiko Kanazashi

• Shizuoka High School, Japan

autor

Hiroyuki Okazaki

• Shinshu University, Nagano, Japan

autor

Yasunari Shidama

• Shinshu University, Nagano, Japan

Bibliografia

• [1] Józef Białas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990.
• [2] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
• [3] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
• [4] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
• [5] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
• [6] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
• [7] Noboru Endou. Banach algebra of bounded complex linear operators. Formalized Mathematics, 12(3):237-242, 2004.
• [8] Noboru Endou. Complex linear space and complex normed space. Formalized Mathematics, 12(2):93-102, 2004.
• [9] Noboru Endou. Complex valued functions space. Formalized Mathematics, 12(3):231-235, 2004.
• [10] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.
• [11] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
• [12] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
• [13] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
• [14] Takashi Mitsuishi, Katsumi Wasaki, and Yasunari Shidama. Property of complex functions. Formalized Mathematics, 9(1):179-184, 2001.
• [15] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
• [16] 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]
• [17] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
• [18] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
• [19] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
• [20] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
• [21] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

Identyfikatory

DOI

10.2478/v10037-011-0019-0