It is shown that if α,ζ are ordinals such that 1 ≤ 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 for 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.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
CONTENTS 0. Introduction.................................................................................................5 1. Preliminaries...............................................................................................6 2. Weakly null sequences and the l¹-index......................................................9 3. Comparison with the l¹-index.....................................................................12 4. Construction of weakly null sequences with large oscillation index............21 5. Reflexive spaces with large oscillation index.............................................33 6. Comparison with the averaging index........................................................37 References....................................................................................................43
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.