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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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On weak criteria for vector-valued holomorphy
by
Karl-Goswin Grosse-Erdmann
Fachbereich Mathematik, Fernuniversität Hagen, Hagen, Germany

Let E be a locally complete locally convex space and f an E-valued function on a complex domain. In a previous result by the author it was shown that for f to be holomorphic it suffices that

(a) x' o f is holomorphic for each continuous linear functional x' from a separating subset of E', and that

(b) f is locally bounded.

Recently, Arendt and Nikolski have given a new and short proof of this result (in the case of Fréchet spaces). We shall here give another new short proof that also allows several extensions of the result.

Date received: November 30, 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-50.