AMCA: Complemented subspaces of spaces of multilinear forms and tensor products. by Felix Cabello-Sanchez

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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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Complemented subspaces of spaces of multilinear forms and tensor products.
by
Félix Cabello-Sánchez
Departamento de Matemáticas, Universidad de Extremadura, Badajoz 06071, España.

Among other things, we show that L_q is isometric to a 1-complemented subspace of the space of multilinear forms on L_p₁×...×L_{p_n}, where q >= 1 is given by 1/p₁+... +1/p_n+1/q=1. The proof strongly depends on the L_\infty-module structure of the spaces L_p and uses in a critical way the amenability of the Banach algebra L_\infty. Some applications to the main diagonal subspace (of tensor products) are given.

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Date received: April 12, 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 Mathematical Conference Abstracts. Document # caey-21.