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On Baire-1/4 functions and spreading models

Part of: Linear function spaces and their duals

Published online by Cambridge University Press:  26 February 2010

Vassiliki Farmaki
Vassiliki Farmaki
Affiliation:
Department of Mathematics, University of Athens, Panepistemiopolis, llissia, Greece.
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Abstract

We prove a characterization of functions in B1/4(K)\C(K), where K is a compact metric space in terms of c0-spreading models, answering a Problem of R. Haydon, E. Odell and H. Rosenthal. Beginning with B1/4(K) we define a decreasing family (Vξ(K),║ · ║ξ)1≤ξ<ω1 of Banach spaces whose intersection is DBSC(K) and we prove an analogous stronger property for the functions in Vξ(K)\C(K). Defining the s-spreading model-index, we classify B1/4;(K) and we prove that s-SM[F]>ξ for every F∈ Vξ(K). Also we classify the separable Banach spaces by defining the c0-SM-index which measures the degree to which they have sequences with extending spreading models equivalent to the usual basis of c0. We give examples of Baire-1 functions and reflexive spaces with arbitrary large indices.

MSC classification

Secondary: 46E99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 41 , Issue 2 , December 1994 , pp. 251 - 265
Copyright
Copyright © University College London 1994

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