Classifications of Baire functions and spreading models
Author:
V. Farmaki
Journal:
Trans. Amer. Math. Soc. 345 (1994), 819831
MSC:
Primary 46B20; Secondary 26A21, 46B15, 46E15
MathSciNet review:
1262339
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Abstract: We prove that if for a bounded function f defined on a compact space K there exists a bounded sequence of continuous functions, with spreading model of order , , equivalent to the summing basis of , converging pointwise to f, then (the index as defined by A. Kechris and A. Louveau). As a corollary of this result we have that the Banach spaces , , which previously defined by the author, consist of functions with rank greater than . For the case we have the equality of these classes. For every countable ordinal number we construct a function S with . Defining the notion of nullcoefficient sequences of order , , we prove that every bounded sequence of continuous functions converging pointwise to a function f with is a nullcoefficient sequence of order . As a corollary to this we have the following spreading model theorem: Every nontrivial, weakCauchy sequence in a Banach space either has a convex block subsequence generating a spreading model equivalent to the summing basis of or is a nullcoefficient sequence of order 1.
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DOI:
http://dx.doi.org/10.1090/S00029947199412623391
PII:
S 00029947(1994)12623391
Article copyright:
© Copyright 1994
American Mathematical Society
