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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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Several kinds of strongly omnipresent operators
by
Luis Bernal-Gonzalez
Departamento de Analisis Matematico. Facultad de Matematicas. Avda.Reina Mercedes. Apdo.1160. 41080-SEVILLA (Spain)
Coauthors: Maria del Carmen Calderon Moreno (Universidad de Sevilla, Spain), Karl-Goswin Grosse-Erdmann (FernUniversitat Hagen, Germany)

Inspired by the notion of holomorphic monster due to W. Luh and K.G. Grosse-Erdmann, the new concept of strongly omnipresent (SOP) operator is introduced. If G is a domain in the complex plane, we say that a (non necessarily linear) selfmapping T on H(G) (= the space of holomorphic functions on G) is a SOP operator whenever the set of T-monsters is residual in H(G), and a function f in H(G) is said to be a T-monster whenever given any point t in the boundary of G and any function g holomorphic in the unit disk D there exist sequences (an) and (bn), tending to zero and t respectively, such that (Tf(anz + bn)) tends to g(z) compactly on D. Our aim is to present several concrete examples of SOP operators (differential, integral and composition operators, among them), to give some sufficient conditions and to propose several open questions.

(T)

Date received: November 18, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cado-26.