Operators on $C(ω^α)$ which do not preserve $C(ω^α)$
| dc.creator | Alspach, Dale E. | |
| dc.date | 1996-10-17 | |
| dc.date.accessioned | 2026-07-07T09:15:38Z | |
| dc.date.available | 2026-07-07T09:15:38Z | |
| dc.description | It is shown that if $α,ζ$ are ordinals such that $1\leq ζ<α<ζω,$ then there is an operator from $C(ω^{ω^α})$ onto itself such that if $Y$ is a subspace of $C(ω^{ω^α})$ which is isomorphic to $C(ω^{ω^α})$ $,$ 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 any operator from $C(ω^{ω^α})$ onto itself there is a subspace of $C(ω^{ω^α})$ which is isomorphic to $% C(ω^{ω^α})$ on which the operator is an isomorphism. | |
| dc.identifier | https://arxiv.org/abs/math/9610215 | |
| dc.identifier | http://arxiv.org/abs/math/9610215 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153081 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B03 | |
| dc.title | Operators on $C(ω^α)$ which do not preserve $C(ω^α)$ | |
| dc.type | text |