Twisted sums with C(K) spaces

If X is a separable Banach space, we consider the existence of non-trivial twisted sums 0\to C(K)\to Y\to X\to 0, where K=[0,1] or \omega^{\omega}. For the case K=[0,1] we show that there exists a twisted sum whose quotient map is strictly singular if and only if X contains no copy of \ell_1. If K=\...

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Veröffentlicht in:	Transactions of the American Mathematical Society 2003-11, Vol.355 (11), p.4523-4541
Hauptverfasser:	Sánchez, F. Cabello, Castillo, J. M. F., Kalton, N. J., Yost, D. T.
Format:	Artikel
Sprache:	eng
Schlagworte:	Banach space Cardinality Continuous functions Counterexamples Exact sciences and technology Functional analysis Linear transformations Mathematical analysis Mathematical sequences Mathematical theorems Mathematics Quotients Sciences and techniques of general use Separable spaces
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