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Operators on C(ω^α) which do not preserve C(ω^α)

100%

Alspach D. E.

Fundamenta Mathematicae

1997

tom 153

nr 1

81-98

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.

Complexity of weakly null sequences

89%

Alspach D. E., Argyros S.

Instytut Matematyczny Polskiej Akademii Nauk

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

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1 Fundamenta Mathematicae

2 Alspach D. E.

1 Argyros S.

1 1997

1 1992

Wyniki wyszukiwania

Operators on C(ω^α) which do not preserve C(ω^α)

Complexity of weakly null sequences