The Property (DN) and the Exponential Representation of Holomorphic Functions.
The property (Hu) and (Ω) with the exponential representation of holomorphic functions.
The main aim of this paper is to prove that a nuclear Fréchet space E has the property (Hu) (resp. (Ω)) if and only if every holomorphic function on E (resp. on some dense subspace of E) can be written in the exponential form.
The space of countably simple bounded functions with values in a DF-space.
The space of exponentially decreasing entire functions and its application to solvability
The space of real-analytic functions has no basis
Let Ω be an open connected subset of . We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.
The Steinitz theorem on rearrangement of series for nuclear spaces.
The three space problem for locally bounded -spaces
The uniform classification of boundedly compact locally convex spaces
Topological localization in Fréchet algebras.
Topological tensor products of a Fréchet-Schwartz space and a Banach space
We exhibit examples of countable injective inductive limits E of Banach spaces with compact linking maps (i.e. (DFS)-spaces) such that is not an inductive limit of normed spaces for some Banach space X. This solves in the negative open questions of Bierstedt, Meise and Hollstein. As a consequence we obtain Fréchet-Schwartz spaces F and Banach spaces X such that the problem of topologies of Grothendieck has a negative answer for . This solves in the negative a question of Taskinen. We also give...
Two problems of valdivia on distinguished Frechet spaces.