On Baire-1/4 functions

Author:
Vassiliki Farmaki

Journal:
Trans. Amer. Math. Soc. **348** (1996), 4023-4041

MSC (1991):
Primary 46B03; Secondary 46B25

DOI:
https://doi.org/10.1090/S0002-9947-96-01719-9

MathSciNet review:
1373633

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Abstract: We give descriptions of the spaces (i.e. the space of differences of bounded semicontinuous functions on ) and especially of (defined by Haydon, Odell and Rosenthal) as well as for the norms which are defined on them. For example, it is proved that a bounded function on a metric space belongs to if and only if the -oscillation, , of is bounded and in this case . Also, we classify into a decreasing family of Banach spaces whose intersection is equal to and . These spaces are characterized by spreading models of order equivalent to the summing basis of , and for every function in it is valid that is bounded. Finally, using the notion of null-coefficient of order sequence, we characterize the Baire-1 functions not belonging to .

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Additional Information

**Vassiliki Farmaki**

Affiliation:
Department of Mathematics, Panepistimiopolis, 15784, Athens, Greece

Email:
vgeorgil@atlas.uoa.gr

DOI:
https://doi.org/10.1090/S0002-9947-96-01719-9

Received by editor(s):
August 22, 1994

Article copyright:
© Copyright 1996
American Mathematical Society