Operators on C(ω^α) which do not preserve C(ω^α)
Alspach, Dale
Fundamenta Mathematicae, Tome 154 (1997), p. 81-98 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:212216 
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     author = {Dale Alspach},
     title = {Operators on C($\omega$^$\alpha$) which do not preserve C($\omega$^$\alpha$)},
     journal = {Fundamenta Mathematicae},
     volume = {154},
     year = {1997},
     pages = {81-98},
     zbl = {0898.46009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv153i1p81bwm}
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Alspach, Dale. Operators on C(ω^α) which do not preserve C(ω^α). Fundamenta Mathematicae, Tome 154 (1997) pp. 81-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv153i1p81bwm/

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