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Higher-dimensional weak amenability

B. Johnson (1997)

Studia Mathematica

Bade, Curtis and Dales have introduced the idea of weak amenability. A commutative Banach algebra A is weakly amenable if there are no non-zero continuous derivations from A to A*. We extend this by defining an alternating n-derivation to be an alternating n-linear map from A to A* which is a derivation in each of its variables. Then we say that A is n-dimensionally weakly amenable if there are no non-zero continuous alternating n-derivations on A. Alternating n-derivations are the same as alternating...

Homogeneous algebras on the circle. I. Ideals of analytic functions

Colin Bennett, John E. Gilbert (1972)

Annales de l'institut Fourier

Let 𝒜 be a homogeneous algebra on the circle and 𝒜 + the closed subalgebra of 𝒜 of functions having analytic extensions into the unit disk D . This paper considers the structure of closed ideals of 𝒜 + under suitable restrictions on the synthesis properties of 𝒜 . In particular, completely characterized are the closed ideals in 𝒜 + whose zero sets meet the circle in a countable set of points. These results contain some previous results of Kahane and Taylor-Williams obtained independently.

Homogeneous algebras on the circle. II. Multipliers, Ditkin conditions

Colin Bennett, John E. Gilbert (1972)

Annales de l'institut Fourier

This paper considers the Lipschitz subalgebras Λ ( α , p , 𝒜 ) of a homogeneous algebra on the circle. Interpolation space theory is used to derive estimates for the multiplier norm on closed primary ideals in Λ ( α , p ; 𝒜 ) , α [ α ] . From these estimates the Ditkin and Analytic Ditkin conditions for Λ ( α , p ; 𝒜 ) follow easily. Thus the well-known theory of (regular) Banach algebras satisfying the Ditkin condition applies to Λ ( α ; , p ; 𝒜 ) as does the theory developed in part I of this series which requires the Analytic Ditkin condition.Examples are discussed...

Homogenous Banach spaces on the unit circle.

Thomas Vils Pedersen (2000)

Publicacions Matemàtiques

We prove that a homogeneous Banach space B on the unit circle T can be embedded as a closed subspace of a dual space Ξ*B contained in the space of bounded Borel measures on T in such a way that the map B → Ξ*B defines a bijective correspondence between the class of homogeneous Banach spaces on T and the class of prehomogeneous Banach spaces on T.We apply our results to show that the algebra of all continuous functions on T is the only homogeneous Banach algebra on T in which every closed ideal has...

Homomorphisms on algebras of Lipschitz functions

Fernanda Botelho, James Jamison (2010)

Studia Mathematica

We characterize a class of *-homomorphisms on Lip⁎(X,𝓑(𝓗 )), a non-commutative Banach *-algebra of Lipschitz functions on a compact metric space and with values in 𝓑(𝓗 ). We show that the zero map is the only multiplicative *-preserving linear functional on Lip⁎(X,𝓑(𝓗 )). We also establish the algebraic reflexivity property of a class of *-isomorphisms on Lip⁎(X,𝓑(𝓗 )).

Homotonic algebras

Michael Cwikel, Moshe Goldberg (2009)

Studia Mathematica

An algebra 𝓐 of real- or complex-valued functions defined on a set T shall be called homotonic if 𝓐 is closed under taking absolute values, and for all f and g in 𝓐, the product f × g satisfies |f × g| ≤ |f| × |g|. Our main purpose in this paper is two-fold: to show that the above definition is equivalent to an earlier definition of homotonicity, and to provide a simple inequality which characterizes submultiplicativity and strong stability for weighted sup norms on homotonic algebras.

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