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Fundamenta Mathematicae

1997 | 153 | 1 | 81-98
Tytuł artykułu

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

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
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EN
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
81-98
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-10-22
Twórcy
autor
Bibliografia
• [A1] D. E. Alspach, Quotients of C[0,1] with separable dual, Israel J. Math. 29 (1978), 361-384.
• [A2] D. E. Alspach, C(K) norming subsets of C[0,1]*, Studia Math. 70 (1981), 27-61.
• [BP] C. Bessaga and A. Pełczyński, Spaces of continuous functions IV, Studia Math. 19 (1960), 53-62.
• [BD] E. Bishop and K. de Leeuw, The representation of linear functionals by measures on sets of extreme points, Ann. Inst. Fourier (Grenoble) 9 (1959), 305-331.
• [B] J. Bourgain, The Szlenk index and operators on C(K)-spaces, Bull. Soc. Math. Belg. Sér. B 31 (1979), 87-117.
• [G] I. Gasparis, Quotients of C(K) spaces, dissertation, The University of Texas, 1995.
• [G1] I. Gasparis, Operators that do not preserve C(α)-spaces, preprint.
• [MS] S. Mazurkiewicz et W. Sierpiński, Contributions à la topologie des ensembles dénombrables, Fund. Math. 1 (1920), 17-27.
• [P] A. Pełczyński, On strictly singular and cosingular operators I. Strictly singular and strictly cosingular operators on C(S) spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1965), 31-36.
• [W] J. Wolfe, C(α) preserving operators on C(K) spaces, Trans. Amer. Math. Soc. 273 (1982), 705-719.
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Bibliografia
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