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.
The Bornological Topology on the Space of Holomorphic Mappings on a Banach Space.
The boundedness principle for lattice-normed spaces.
The canonical seminorm on Weak L¹
The chi function in generalized summability
The Choquet integral representation in the affine vector-valued case.
The class of convolution operators on the Marcinkiewicz spaces
Let denote the operator-norm closure of the class of convolution operators where is a suitable function space on . Let be the closed subspace of regular functions in the Marinkiewicz space , . We show that the space is isometrically isomorphic to and that strong operator sequential convergence and norm convergence in coincide. We also obtain some results concerning convolution operators under the Wiener transformation. These are to improve a Tauberian theorem of Wiener on .
The closed graph theorem for multilinear mappings.
The closed neighborhood and filter conditions in solid sequence spaces.
The compact endomorphisms of the metric linear spaces
The Components of a Positive Operator.