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Acta Mathematica Sinica, 2000
The systematic study of real Banach *-algebras are given in this paper. It is shown that \textit{J. W. M. Ford}'s lemma [see J. Lond. Math. Soc. 42, 521-522 (1967; Zbl 0145.38702)] and \textit{V. Pták}'s inequality [see Bull. Lond. Math. Soc. 2, 327-334 (1970; Zbl 0209.44403)] hold in the real case and the (real) linear span of unitary elements ...
Li, Bingren, Tam, Pingkwan
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The systematic study of real Banach *-algebras are given in this paper. It is shown that \textit{J. W. M. Ford}'s lemma [see J. Lond. Math. Soc. 42, 521-522 (1967; Zbl 0145.38702)] and \textit{V. Pták}'s inequality [see Bull. Lond. Math. Soc. 2, 327-334 (1970; Zbl 0209.44403)] hold in the real case and the (real) linear span of unitary elements ...
Li, Bingren, Tam, Pingkwan
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Mathematics of the USSR-Izvestiya, 1980
This paper studies the structure of biprojective semisimple Banach algebras having the approximation property. It is shown that every such algebra can be represented as the completion of a direct sum of topologically simple biprojective Banach algebras.
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This paper studies the structure of biprojective semisimple Banach algebras having the approximation property. It is shown that every such algebra can be represented as the completion of a direct sum of topologically simple biprojective Banach algebras.
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Canadian Journal of Mathematics, 1964
Let A be a complex Banach algebra and Lr (Ll) be the lattice of all closed right (left) ideals in A. Following Tomiuk (5), we say that A is a right complemented algebra if there exists a mapping I —> IP of Lτ into Lr such that if I ∊ Lr, then I ∩ Ip = (0), (Ip)p = I, I ⴲ Ip = A and if I1, I2 ∊ Lr with I1 ⊆ I2 then .If in a Banach algebra A every ...
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Let A be a complex Banach algebra and Lr (Ll) be the lattice of all closed right (left) ideals in A. Following Tomiuk (5), we say that A is a right complemented algebra if there exists a mapping I —> IP of Lτ into Lr such that if I ∊ Lr, then I ∩ Ip = (0), (Ip)p = I, I ⴲ Ip = A and if I1, I2 ∊ Lr with I1 ⊆ I2 then .If in a Banach algebra A every ...
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2022
Abstract This chapter introduces the study of Banach algebras, and sets the tone for the discussion that continues later in Chapters 11–13. We present and investigate the spectrum of elements in Banach algebras. We next discuss commutative Banach algebras as well as the Gelfand representation.
Shmuel Kantorovitz, Ami Viselter
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Abstract This chapter introduces the study of Banach algebras, and sets the tone for the discussion that continues later in Chapters 11–13. We present and investigate the spectrum of elements in Banach algebras. We next discuss commutative Banach algebras as well as the Gelfand representation.
Shmuel Kantorovitz, Ami Viselter
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2003
Abstract If X is a Banach space, the Banach space B(X) (cf. Notation 4.3) is also an algebra under the composition of operators as multiplication.
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Abstract If X is a Banach space, the Banach space B(X) (cf. Notation 4.3) is also an algebra under the composition of operators as multiplication.
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Variational algorithms for linear algebra
Science Bulletin, 2021Xiaosi Xu, Jinzhao Sun, Suguru Endo
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