On a Problem of Bellenot and Dubinsky.
On automatic boundedness of Nemytskiĭ set-valued operators
Let X, Y be two separable F-spaces. Let (Ω,Σ,μ) be a measure space with μ complete, non-atomic and σ-finite. Let be the Nemytskiĭ set-valued operator induced by a sup-measurable set-valued function . It is shown that if maps a modular space into subsets of a modular space , then is automatically modular bounded, i.e. for each set K ⊂ N(L(Ω,Σ,μ;X)) such that we have .
On barycentrs in non-compact sets
On bases in the spaces of Dirichlet transformations of finite order
On Compactness in Locally Convex Spaces.
On complemented subspaces of some Köthe spaces of infinite type.
On exact sequences of quojections.
We give some general exact sequences for quojections from which many interesting representation results for standard twisted quojections can be deduced. Then the methods are also generalized to the case of nuclear Fréchet spaces.
On extending and lifting continuous linear mappings in topological vector spaces
On isomorphic classification of tensor products [Book]
On meromorphic functions with values in locally convex spaces
On metrizable abelian groups with a completeness-type property
On non-primary Fréchet Schwartz spaces
Let E be a Fréchet Schwartz space with a continuous norm and with a finite-dimensional decomposition, and let F be any infinite-dimensional subspace of E. It is proved that E can be written as G ⨁ H where G and H do not contain any subspace isomorphic to F. In particular, E is not primary. If the subspace F is not normable then the statement holds for other quasinormable Fréchet spaces, e.g., if E is a quasinormable and locally normable Köthe sequence space, or if E is a space of holomorphic functions...
On some classes of linear topological spaces
On some dense subspaces of topological linear spaces
On suprema of metrizable vector topologies with trivial dual
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 class of entire Dirichlet functions of several complex variables having finite order point
On the connectedness of the set of fixed points of a compact operator in the Fréchet space
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.