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.
The concept of boundedness and the Bohr compactification of a MAP Abelian group
Let G be a maximally almost periodic (MAP) Abelian group and let ℬ be a boundedness on G in the sense of Vilenkin. We study the relations between ℬ and the Bohr topology of G for some well known groups with boundedness (G,ℬ). As an application, we prove that the Bohr topology of a topological group which is topologically isomorphic to the direct product of a locally convex space and an -group, contains “many” discrete C-embedded subsets which are C*-embedded in their Bohr compactification. This...
The continuity of superposition operators on some sequence spaces defined by moduli
Let and be solid sequence spaces. For a sequence of modulus functions let . Given another sequence of modulus functions , we characterize the continuity of the superposition operators from into for some Banach sequence spaces and under the assumptions that the moduli
The coordinatewise uniformly Kadec-Klee property in some Banach spaces.
The density condition and the strong dual density condition by operator.
The aim of the present article is to introduce and investigate topological properties by operator. We obtain good stability properties for the density condition and the strong dual density condition by taking injective tensor products. Further we analyze the connection to (DF)-properties by operator.
The density condition in projective tensor products.
In this paper we modify a construction due to J. Taskinen to get a Fréchet space F which satisfies the density condition such that the complete injective tensor product l2 x~eF'b does not satisfy the strong dual density condition of Bierstedt and Bonet. In this way a question that remained open in Heinrichs (1997) is solved.
The density condition in quotients of quasinormable Fréchet spaces
It is proved that a separable Fréchet space is quasinormable if, and only if, every quotient space satisfies the density condition of Heinrich. This answers positively a conjecture of Bonet and Dí az in the class of separable Fréchet spaces.
The density condition in quotients of quasinormable Fréchet spaces, II.
It is proved that a Fréchet space is quasinormable if, and only if, every quotient space satisfies the density condition of Heinrich. This answers positively a conjecture of Bonet and Díaz
The Density Condition in Subspaces and Quotients of Frechet Spaces.
The diametral dimension of the spaces of Whitney jets on sequences of points.
The differences of inclusion map operators between rearrangement invariant spaces on finite and sigma-finite measure spaces.