On pseudonormability of some particular classes of spaces
On Schwartz groups
We introduce a notion of a Schwartz group, which turns out to be coherent with the well known concept of a Schwartz topological vector space. We establish several basic properties of Schwartz groups and show that free topological Abelian groups, as well as free locally convex spaces, over hemicompact k-spaces are Schwartz groups. We also prove that every hemicompact k-space topological group, in particular the Pontryagin dual of a metrizable topological group, is a Schwartz group.
On Some Spaces Of Analytic Functions And Their Duality Relations.
On Tensor Product Characterization of Nuclear Spaces.
On the algebra of smooth operators
Let s be the space of rapidly decreasing sequences. We give the spectral representation of normal elements in the Fréchet algebra L(s',s) of so-called smooth operators. We also characterize closed commutative *-subalgebras of L(s',s) and establish a Hölder continuous functional calculus in this algebra. The key tool is the property (DN) of s.
On the BAP in Fréchet Schwartz Spaces and Their Duals.
On the Completition of (LF)-Spaces.
On the derived tensor product functors for (DF)- and Fréchet spaces
For a (DF)-space E and a tensor norm α we investigate the derivatives of the tensor product functor from the category of Fréchet spaces to the category of linear spaces. Necessary and sufficient conditions for the vanishing of , which is strongly related to the exactness of tensored sequences, are presented and characterizations in the nuclear and (co-)echelon cases are given.
On the existence of unitary representations of commutative nuclear Lie groups
On the extension of holomorphic functions on a locally convex space
On the extension of holomorphic maps on locally convex spaces with values in Fréchet spaces
On the extension of Lipschitz maps with values in a Fréchet space
On the functors Ext¹(E,F) for Fréchet spaces
On the Glicksberg theorem for locally quasi-convex Schwartz groups
We prove that every locally quasi-convex Schwartz group satisfies the Glicksberg theorem for weakly compact sets.
On the relation of the bounded approximation property and a finite dimensional decomposition in nuclear Fréchet spaces
On the splitting of twisted sums, and the three space problem for local convexity
On the subspaces of Fréchet Montel spaces and of the strong duals of Fréchet Montel spaces.
On the three-space property for locally convex spaces.
On the three-space-problem for topological vector spaces.
On Weighted Inductive Limits of Spaces of Continuous Function.