Classifications of Baire- functions and -spreading models

Author:
V. Farmaki

Journal:
Trans. Amer. Math. Soc. **345** (1994), 819-831

MSC:
Primary 46B20; Secondary 26A21, 46B15, 46E15

DOI:
https://doi.org/10.1090/S0002-9947-1994-1262339-1

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 null-coefficient sequences of order , , we prove that every bounded sequence of continuous functions converging pointwise to a function *f* with is a null-coefficient sequence of order . As a corollary to this we have the following -spreading model theorem: Every nontrivial, weak-Cauchy sequence in a Banach space either has a convex block subsequence generating a spreading model equivalent to the summing basis of or is a null-coefficient sequence of order 1.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1262339-1

Article copyright:
© Copyright 1994
American Mathematical Society