Search results for "holomorphic mapping"
showing 2 items of 2 documents
The Spectrum of Analytic Mappings of Bounded Type
2000
Abstract A Banach space E is said to be (symmetrically) regular if every continuous (symmetric) linear mapping from E to E ′ is weakly compact. For a complex Banach space E and a complex Banach algebra F , let H b ( E , F ) denote the algebra of holomorphic mappings from E to F which are bounded on bounded sets. We endow H b ( E , F ) with the usual Frechet topology. M ( H b ( E , F ), F ) denotes the set of all non-null continuous homomorphisms from H b ( E , F ) to F . A subset of G EF on which the extension of Zalduendo is multiplicative is presented and it is shown that, in general, the sets G EF and M ( H b ( E , F ), F ) do not coincide. We prove that if E is symmetrically regu…
On approximating curves associated with nonexpansive mappings
2011
Let X be a Banach space with metric d. Let T, N : X → X be a strict d-contraction and a d-nonexpansive map, respectively. In this paper we investigate the properties of the approximating curve associated with T and N. Moreover, following [3], we consider the approximating curve associated with a holomorphic map f : B → α B and a ρ-nonexpansive map M : B → B, where B is the open unit ball of a complex Hilbert space H, ρ is the hyperbolic metric defined on B and 0 ≤ α < 1. We give conditions on f and M for this curve to be injective, and we show that this curve is continuous.