Tame Spaces and Power Series Spaces.
Tensor Product of Several Spaces and Nuclearity.
Tensor Products and Banach Ideals of p-Compact Operators.
Tensor products of Hilbert modules over locally -algebras
In this paper the tensor products of Hilbert modules over locally -algebras are defined and their properties are studied. Thus we show that most of the basic properties of the tensor products of Hilbert -modules are also valid in the context of Hilbert modules over locally -algebras.
Tensor Sequences and Inductive Limits with Local Partition of Unity.
The approximation property of some vector valued Sobolev-Slobodeckij spaces.
The dual of the space of holomorphic functions on locally closed convex sets.
Let H(Q) be the space of all the functions which are holomorphic on an open neighbourhood of a convex locally closed subset Q of CN, endowed with its natural projective topology. We characterize when the topology of the weighted inductive limit of Fréchet spaces which is obtained as the Laplace transform of the dual H(Q)' of H(Q) can be described by weighted sup-seminorms. The behaviour of the corresponding inductive limit of spaces of continuous functions is also investigated.
The non-archimedean space
The projective limit functor for spectra of webbed spaces
We study Palamodov's derived projective limit functor Proj¹ for projective spectra consisting of webbed locally convex spaces introduced by Wilde. This class contains almost all locally convex spaces appearing in analysis. We provide a natural characterization for the vanishing of Proj¹ which generalizes and unifies results of Palamodov and Retakh for spectra of Fréchet and (LB)-spaces. We thus obtain a general tool for solving surjectivity problems in analysis.
The Property (DN) and the Exponential Representation of Holomorphic Functions.
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.
Topological classification of strong duals to nuclear (LF)-spaces
We show that the strong dual X’ to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: , , , , or , where and . In particular, the Schwartz space D’ of distributions is homeomorphic to . As a by-product of the proof we deduce that each infinite-dimensional locally convex space which is a direct limit of metrizable compacta is homeomorphic either to or to . In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic either...
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...
Topologies and Bornologies Determined by Operator Ideals.
Triplets conucléaires en théorie des champs