Wyniki wyszukiwania

1

Uniqueness of complete norms for quotients of Banach function algebras

100%

Bade W. G., Dales H. G.

Studia Mathematica

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1993

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tom 106

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nr 3

289-302

EN

We prove that every quotient algebra of a unital Banach function algebra A has a unique complete norm if A is a Ditkin algebra. The theorem applies, for example, to the algebra A (Γ) of Fourier transforms of the group algebra $L^1(G)$ of a locally compact abelian group (with identity adjoined if Γ is not compact). In such algebras non-semisimple quotients $A(Γ)/\overline{J(E)}$ arise from closed subsets E of Γ which are sets of non-synthesis. Examples are given to show that the condition of Ditkin cannot be relaxed. We construct a variety of mutually non-equivalent norms for quotients of the Mirkil algebra M, which fails Ditkin's condition at only one point of $Φ_M$.

2

Raising bounded groups and splitting of radical extensions of commutative Banach algebras

81%

Bade W. G., P. C. Curtis, Jr., Sinclair A. M.

Studia Mathematica

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2000

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tom 141

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nr 1

85-98

EN

Let A be a commutative unital Banach algebra and let A/ℛ be the quotient algebra of A modulo its radical ℛ. This paper is concerned with raising bounded groups in A/ℛ to bounded groups in the algebra A. The results will be applied to the problem of splitting radical extensions of certain Banach algebras.

3

Continuity of derivations from radical convolution algebras

60%

Bade W. G., Dales H. G.

Studia Mathematica

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1989-1990

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tom 95

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nr 1

59-91

Ograniczanie wyników

3 Studia Mathematica

3 Bade W. G.

2 Dales H. G.

1 P. C. Curtis, Jr.

1 Sinclair A. M.

1 2000

1 1993

1 1989

Uniqueness of complete norms for quotients of Banach function algebras

Raising bounded groups and splitting of radical extensions of commutative Banach algebras

Continuity of derivations from radical convolution algebras