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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 linear functionals on the space of Borel vector measures

Pola Siwek (2008)

Annales Polonici Mathematici

We study properties of the space ℳ of Borel vector measures on a compact metric space X, taking values in a Banach space E. The space ℳ is equipped with the Fortet-Mourier norm | | · | | and the semivariation norm ||·||(X). The integral introduced by K. Baron and A. Lasota plays the most important role in the paper. Investigating its properties one can prove that in most cases the space ( , | | · | | ) * is contained in but not equal to the space (ℳ,||·||(X))*. We obtain a representation of the continuous functionals on...

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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