We study the presence of copies of ln p ’s uniformly in the spaces 2(C[0, 1],X) and 1(C[0, 1],X). By using Dvoretzky’s theorem we deduce that if X is an infinite- dimensional Banach space, then 2(C[0, 1],X) contains p2-uniformly copies of ln∞’s and 1(C[0, 1],X) contains -uniformly copies of ln 2 ’s for all > 1. As an application, we show that if X is an infinite-dimensional Banach space then the spaces 2(C[0, 1],X) and 1(C[0, 1],X) are distinct, extending the well-known result that the spaces 2(C[0, 1],X) and N(C[0, 1],X) are distinct., Dumitru Popa., and Seznam literatury
In this paper we give some sufficient conditions for the adjoint of a weighted composition operator on a Hilbert space of analytic functions to be hypercyclic.
For subspaces, X and Y , of the space, D, of all derivatives M(X, Y ) denotes the set of all g ∈ D such that fg ∈ Y for all f ∈ X. Subspaces of D are defined depending on a parameter p ∈ [0, ∞]. In Section 6, M(X, D) is determined for each of these subspaces and in Section 7, M(X, Y ) is found for X and Y any of these subspaces. In Section 3, M(X, D) is determined for other spaces of functions on [0, 1] related to continuity and higher order differentiation.
Spaces Oq, q ∈ N, of multipliers of temperate distributions introduced in an earlier paper of the first author are expressed as inductive limits of Hilbert spaces.
Description of multiplication operators generated by a sequence and composition operators induced by a partition on Lorentz sequence spaces l(p, q), 1 < p ≤ ∞, 1 ≤ q ≤ ∞ is presented.
In this paper we analyse a definition of a product of Banach spaces that is naturally associated by duality with a space of operators that can be considered as a generalization of the notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different fields of functional analysis that can be seen as instances of the abstract one when a particular product is considered. Some relevant examples and applications are shown, regarding pointwise products of Banach function spaces, spaces of integrable functions with respect to vector measures, spaces of operators, multipliers on Banach spaces of analytic functions and spaces of Lipschitz functions., Enrique A. Sánchez Pérez., and Obsahuje seznam literatury