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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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Domination by strictly-singular and disjointly strictly-singular operators.
by
Julio Flores
Departamento de Análisis Matemático (Universidad Complutense)
Coauthors: Francisco L. Hernández (Universidad Complutense)

We consider the problem of domination by positive strictly-singular operators and disjointly strictly-singular operators on Banach lattices. Precisely, given E and F Banach lattices and two positive operators 0 <= S <= T:E --> F, which conditions on E and F guarantee that T strictly-singular (resp. disjointly strictly-singular) implies that S is strictly-singular (resp. disjointly strictly-singular)? For instance, we show that T disjointly strictly-singular implies S disjointly strictly-singular provided the norm on F is order continuous. Also, if F has an order continuous norm and E is q-concave and p-convex for some 1 < p, q < \infty, then T strictly-singular implies S strictly-singular.

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Date received: March 23, 2000

Copyright © 2000 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 # caei-47.