On complete, precompact and compact sets.
Completeness criterion of W. Robertson is generalized. Applications to vector valued sequences and to spaces of linear mappings are given.
Surjective convolution operators on spaces of distributions.
We review recent developments in the theory of inductive limits and use them to give a new and rather easy proof for Hörmander?s characterization of surjective convolution operators on spaces of Schwartz distributions.
Small ball properties for Fréchet spaces.
We give characterizations of certain properties of continuous linear maps between Fréchet spaces, as well as topological properties on Fréchet spaces, in terms of generalizations of Behrends and Kadets small ball property.
Connectedness of the Carathéodory discs for doubly connected domains
We prove that the Carathéodory discs for doubly connected domains in the complex plane are connected.
Extension of vector-valued holomorphic and harmonic functions
We present a unified approach to the study of extensions of vector-valued holomorphic or harmonic functions based on the existence of weak or weak*-holomorphic or harmonic extensions. Several recent results due to Arendt, Nikolski, Bierstedt, Holtmanns and Grosse-Erdmann are extended. An open problem by Grosse-Erdmann is solved in the negative. Using the extension results we prove existence of Wolff type representations for the duals of certain function spaces.
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