is a Grothendieck space
Higher-dimensional weak amenability
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...
Hinfty + LE in several variables.
Holomorphic Approximation in Cm-Norms on Totally Real Compact Sets in Cn.
Holomorphic extension from the sphere to the ball in Hilbert space
Homogeneous algebras on the circle. I. Ideals of analytic functions
Let be a homogeneous algebra on the circle and the closed subalgebra of of functions having analytic extensions into the unit disk . This paper considers the structure of closed ideals of under suitable restrictions on the synthesis properties of . In particular, completely characterized are the closed ideals in 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
This paper considers the Lipschitz subalgebras of a homogeneous algebra on the circle. Interpolation space theory is used to derive estimates for the multiplier norm on closed primary ideals in , . From these estimates the Ditkin and Analytic Ditkin conditions for follow easily. Thus the well-known theory of (regular) Banach algebras satisfying the Ditkin condition applies to as does the theory developed in part I of this series which requires the Analytic Ditkin condition.Examples are discussed...
Homogeneous spaces of compact connected Lie groups which admit nontrivial invariant algebras.
Homogenous Banach spaces on the unit circle.
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...
Homomorphismes d'espaces de Banach de fonctions continues
Homomorphismes discontinus des algèbres de Banach commutatives séparables
Homomorphisms on algebras of Lipschitz functions
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
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.