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IV Iberoamerican Conference on Topology and its Applications (IV CITA)
April 18-21, 2001
University of Coimbra
Coimbra, Portugal

Organizers
Maria Manuel Clementino, Jorge Picado, Lurdes Sousa, Maria João Ferreira, Gonçalo Gutierres, Dirk Hofmann

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Basis separating maps
by
Lawrence Narici
St. John's University, Jamaica, NY 11439, USA
Coauthors: Edward Beckenstein (St. John's University, Staten Island, NY, USA)

Basis Separating Maps

Basis Separating Maps

By way of the Stone-Banach theorem, we know the canonical form for linear isometries A:C( X) --> C( Y) of spaces C( X) and C( Y) of continuous functions on compact spaces X and Y. In this article we develop a canonical form for linear isometries H:X --> Y of Banach spaces X and Y with Schauder bases. We do this by means of the notion of a ``basis separating map'' between X and Y: Given Banach spaces X and Y with Schauder bases { xn} and { yn} , respectively, we say that H:X --> Y, H( \sumn in Nx(n) xn) = \sumn in NHx( n) yn, is ``basis separating'' if for all x=\sumn in Nx( n)xn, y=\sumn in Ny( n) xn in X, x(n) y( n) = 0 for all n in N implies that Hx( n) Hy( n) = 0 for all n in N. A key tool in doing this is showing that associated with a linear basis separating map H, there is a support map h:N --> N\infty. We use it to investigate automatic continuity and canonical forms of basis separating maps.

Date received: January 3, 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 # cafw-05.