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BMS-DMV LIEGE 2001
June 8-10, 2001
University of Liège
Liège, Belgium

Organizers
Klaus D. Bierstedt, J. Schmets

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The space of real analytic functions has no basis
by
Dietmar Vogt
Bergische Universität, Wuppertal
Coauthors: Pawel Doma{n}ski (A. Mickiewicz University, Pozna{n})

Let \Omega be an open subset of Rd. It is shown that the space A(\Omega) of real analytic functions on \Omega has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(\Omega) are finite dimensional. This result has also other interesting consequences. It is based on structural properties of A(\Omega) which are expressed in terms of certain linear topological invariants.

Date received: April 4, 2001

Copyright © 2001 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 # cahh-06.