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Journal of the London Mathematical Society 1998 58(3):679-696; doi:10.1112/S0024610798006619
© 1998 by London Mathematical Society
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© The London Mathematical Society

Maurey's Extension Theorem and Grothendieck's Problème Des Topologies

A. Defant and A. Peris

Fachbereich Mathematik, Carl von Ossietzky Universität Oldenburg D-26111 Oldenburg, Germany. E-mail: defant{at}mathematik.uni-oldenburg.de
Departamento de Matematica, Aplicada ETS Arquitectura, Universidad Politécnica Valencia E-46071 Valencia, Spain. E-mail: aperis{at}pleiades.upv.es

Received 5 October 1995. Revision received 26 October 1996.

Relating geometric notions like type and cotype from local Banach space theory with some important topological invariants for Fréchet spaces (for example the density condition), we prove a version of Maurey's celebrated extension theorem for the category of Fréchet spaces, and apply it to Grothendieck's problème des topologies.


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