Lacunary sets based on Lorentz spaces

Author:
Raymond J. Grinnell

Journal:
Proc. Amer. Math. Soc. **127** (1999), 3547-3556

MSC (1991):
Primary 43A46; Secondary 43A15, 43A25

DOI:
https://doi.org/10.1090/S0002-9939-99-04918-7

Published electronically:
May 13, 1999

MathSciNet review:
1610901

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Abstract | References | Similar Articles | Additional Information

Abstract: A new lacunary set for compact abelian groups is introduced; this is called a set. This set is defined in terms of the Lorentz spaces and is shown to be a generalization of sets and Sidon sets. A number of functional-analytic statements about sets are established by making use of the structural similarities between spaces and Lorentz spaces. These statements are analogous to several well-known properties of a set which are equivalent to the definition of a set. Some general set-theoretic and arithmetic properties of sets are also developed; these properties extend known results on the structure of sets. Open problems and directions for further research are outlined.

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Additional Information

**Raymond J. Grinnell**

Affiliation:
Department of Computer Science, Mathematics & Physics, University of the West Indies, Cave Hill Campus, P.O. Box 64, Bridgetown, Barbados, West Indies

Email:
grinnell@uwichill.edu.bb

DOI:
https://doi.org/10.1090/S0002-9939-99-04918-7

Received by editor(s):
September 5, 1996

Received by editor(s) in revised form:
February 12, 1998

Published electronically:
May 13, 1999

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1999
American Mathematical Society