Displaying similar documents to “Holomorphy types on a Banach spaces”

Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on ( U )

Sean Dineen (1973)

Annales de l'institut Fourier

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This article is devoted to a study of locally convex topologies on H ( U ) (where U is an open subset of the locally convex topological vector space E and H ( U ) is the set of all complex valued holomorphic functions on E ). We discuss the following topologies on H ( U ) : (a) the compact open topology I 0 , (b) the bornological topology associated with I 0 , (c) the ported topology of Nachbin I ω , (d) the bornological topology associated with I ω  ; and ...

Quasinormability of some spaces of holomorphic mappings.

José M. Isidro (1990)

Revista Matemática de la Universidad Complutense de Madrid

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A class of locally convex vector spaces with a special Schauder decomposition is considered. It is proved that the elements of this class, which includes some spaces naturally appearing in infinite dimensional holomorphy, are quasinormable though in general they are neither metrizable nor Schwartz spaces.

A rigid space admitting compact operators

Paul Sisson (1995)

Studia Mathematica

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A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. The first complete rigid space was published in 1981 in [2]. Clearly a rigid space is a trivial-dual space, and admits no compact endomorphisms. In this paper a modification of the original construction results in a rigid space which is, however, the domain space of a compact operator, answering a question that was first raised soon after the existence of complete rigid...