Tensor products and -nuclear spaces in -adic analysis
Tensor products in the category of topological vector spaces are not associative
We show by example that the associative law does not hold for tensor products in the category of general (not necessarily locally convex) topological vector spaces. The same pathology occurs for tensor products of Hausdorff abelian topological groups.
Tensor Products of Banach Lattices.
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.
Tensor stable Fréchet and (DF)-spaces.
In this paper we introduce and investigate classes of Fréchet and (DF)-spaces which constitute a very general frame in which the problem of topologies of Grothendieck and some related dual questions have a positive answer. Many examples of spaces in theses classes are provided, in particular spaces of sequences and functions. New counterexamples to the problems of Grothendieck are given.
Tensorprodukte von stetigen linearen Abbildungen in (F)- und (DCF)-Räumen.
The Abel-type transformations into .
The adjoint theorem on A-spaces.
The algebraic dimension of linear metric spaces and Baire properties of their hyperspaces.
Answering a question of Halbeisen we prove (by two different methods) that the algebraic dimension of each infinite-dimensional complete linear metric space X equals the size of X. A topological method gives a bit more: the algebraic dimension of a linear metric space X equals |X| provided the hyperspace K(X) of compact subsets of X is a Baire space. Studying the interplay between Baire properties of a linear metric space X and its hyperspace, we construct a hereditarily Baire linear metric space...
The approximation property of order p in locally convex spaces.
The approximation property of some vector valued Sobolev-Slobodeckij spaces.
The AR-Property of the spaces of closed convex sets
Let , and be the spaces of all non-empty closed convex sets in a normed linear space X admitting the Hausdorff metric topology, the Attouch-Wets topology and the Wijsman topology, respectively. We show that every component of and the space are AR. In case X is separable, is locally path-connected.
The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces
Following Banakh and Gabriyelyan (2016) we say that a Tychonoff space X is an Ascoli space if every compact subset of is evenly continuous; this notion is closely related to the classical Ascoli theorem. Every -space, hence any k-space, is Ascoli. Let X be a metrizable space. We prove that the space is Ascoli iff is a -space iff X is locally compact. Moreover, endowed with the weak topology is Ascoli iff X is countable and discrete. Using some basic concepts from probability theory and...
The -weak compactness of weak Banach-Saks operators
We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.
The Bade property and the λ-property in spaces of convergent sequences.
In this note we study the Bade property in the C(K,X) and c(X) spaces. We also characterize the spaces X = C(K,R) such that c(X) has the uniform λ-property.
The Banach Envelopes of Besov and Triebel-Lizorkin Spaces and Applications to Partial Differential Equations.
The barrelled topology associated with the compact-open topology on H(U) and H(K)
The basic sequence problem
We construct a quasi-Banach space X which contains no basic sequence.
The behaviour of transformations on sequence spaces.