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Compact homomorphisms between algebras of analytic functions

Richard Aron, Pablo Galindo, Mikael Lindström (1997)

Studia Mathematica

We prove that every weakly compact multiplicative linear continuous map from H ( D ) into H ( D ) is compact. We also give an example which shows that this is not generally true for uniform algebras. Finally, we characterize the spectra of compact composition operators acting on the uniform algebra H ( B E ) , where B E is the open unit ball of an infinite-dimensional Banach space E.

Complementation in spaces of symmetric tensor products and polynomials.

Fernando Blasco (1996)

Extracta Mathematicae

Our aim here is to announce some properties of complementation for spaces of symmetric tensor products and homogeneous continuous polynomials on a locally convex space E that have, in particular, consequences in the study of the property (BB)n,s recently introduced by Dineen [8].

Continuous linear extension operators on spaces of holomorphic functions on closed subgroups of a complex Lie group

Do Duc Thai, Dinh Huy Hoang (1999)

Annales Polonici Mathematici

We show that the restriction operator of the space of holomorphic functions on a complex Lie group to an analytic subset V has a continuous linear right inverse if it is surjective and if V is a finite branched cover over a connected closed subgroup Γ of G. Moreover, we show that if Γ and G are complex Lie groups and V ⊂ Γ × G is an analytic set such that the canonical projection π 1 : V Γ is finite and proper, then R V : O ( Γ × G ) I m R V O ( V ) has a right inverse

Continuous Reinhardt domains from a Jordan viewpoint

L. L. Stachó (2008)

Studia Mathematica

As a natural extension of bounded complete Reinhardt domains in N to spaces of continuous functions, continuous Reinhardt domains (CRD) are bounded open connected solid sets in commutative C*-algebras with respect to the natural ordering. We give a complete parametric description for the structure of holomorphic isomorphisms between CRDs and characterize the partial Jordan triple structures which can be associated with some CRDs. On the basis of these results, we test two conjectures concerning...

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