ArticleOriginal scientific text

Title

Operators on C(ωα) which do not preserve C(ωα)

Authors 1

Affiliations

  1. Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078, U.S.A.

Abstract

It is shown that if α,ζ are ordinals such that 1 ≤ ζ < α < ζω, then there is an operator from C(ωωα) onto itself such that if Y is a subspace of C(ωωα) which is isomorphic to C(ωωα), then the operator is not an isomorphism on Y. This contrasts with a result of J. Bourgain that implies that there are uncountably many ordinals α for which for any operator from C(ωωα) onto itself there is a subspace of C(ωωα) which is isomorphic to C(ωωα) on which the operator is an isomorphism.

Keywords

ordinal index, Szlenk index, Banach space of continuous functions

Bibliography

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Pages:
81-98
Main language of publication
English
Received
1996-10-22
Published
1997
Exact and natural sciences