Asplund Operators on Locally Convex Spaces

We study the relationship between the local Radon-Nikodým property, introduced by Defant [4] as a generalization of the Radon-Nikodým property to duals of locally convex spaces, and the Asplund operators, introduced by Robertson [7]. We also give a characterization of Asplund symmetric tensor products of Banach spaces in terms of Asplund maps.

Invertibility in tensor products of Q-algebras

Linearization of holomorphic mappings on fully nuclear spaces with a basis

In [13] Mazet proved the following result.If U is an open subset of a locally convex space E then there exists a complete locally convex space (U) and a holomorphic mapping δU: U→(U) such that for any complete locally convex space F and any f ɛ ℋ (U;F), the space of holomorphic mappings from U to F, there exists a unique linear mapping Tf: (U)→F such that the following diagram commutes;The space (U) is unique up to a linear topological isomorphism. Previously, similar but less general constructions, have been considered by Ryan [16] and Schottenloher [17].

Weakly uniformly continuous holomorphic functions and the approximation property

Abstract We study the approximation property for spaces of Frechet and Gâteaux holomorphic functions which are weakly uniformly continuous on bounded sets. We show when U is a balanced open subset of a Baire or barrelled metrizable locally convex space, E , that the space of holomorphic functions which are weakly uniformly continuous on U -bounded sets has the approximation property if and only if the strong dual of E , E ′ b , has the approximation property. We also characterise the approximation property for these spaces of vector-valued holomorphic functions in terms of the tensor product of the corresponding space of scalar-valued holomorphic functions and the range space.