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
. We introduce two classes of analytic functions related to conic domains, using a new linear multiplier Dziok-Srivastava operator D n.q,s λ,l (n ∈ N0 = {0, 1, . . .}, q ≤ s + 1; q, s ∈ N0, 0 ≤ α < 1, λ ≥ 0, l ≥ 0). Basic properties of these classes are studied, such as coefficient bounds. Various known or new special cases of our results are also pointed out. For these new function classes, we establish subordination theorems and also deduce some corollaries of these results.
In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.