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1
Content available remote

Uniqueness of complete norms for quotients of Banach function algebras

100%
Bade W. G., Dales H. G.
Studia Mathematica
|
1993
|
tom 106
|
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
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Derivations into iterated duals of Banach algebras

81%
Dales H. G., Ghahramani F., Grønbæek N.
Studia Mathematica
|
1998
|
tom 128
|
nr 1
19-54
EN
We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space $A^{(n)}$ is zero; i.e., $ℋ^1(A,A^{(n)}) = {0}$. Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable; we study group algebras, C*-algebras, Banach function algebras, and algebras of operators. Our results are summarized and some open questions are raised in the final section.
3
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Continuity of derivations from radical convolution algebras

60%
Bade W. G., Dales H. G.
Studia Mathematica
|
1989-1990
|
tom 95
|
nr 1
59-91
4
Content available remote

Pseudo-Banach algebras

50%
Allan G. R., Dales H. G., McClure J. P.
Studia Mathematica
|
1971
|
tom 40
|
nr 1
55-69
5
Content available remote

Eventual continuity in Banach algebras of differentiable functions

50%
Dales H. G.
Studia Mathematica
|
1981
|
tom 70
|
nr 2
101-109
6
Content available remote

Embedding C(X) in an algebra of analytic functions

50%
Dales H. G.
Banach Center Publications
|
1982
|
tom 8
|
nr 1
231-236
7
Content available remote

Local Banach algebras as Henselian rings

40%
Dales H. G.
Studia Mathematica
|
1987
|
tom 87
|
nr 3
281-293
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