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Lacunarity on nonabelian groups and summing operators

Part of: Special classes of linear operators Harmonic analysis in one variable

Published online by Cambridge University Press:  09 April 2009

P. G. Dodds
P. G. Dodds
Affiliation:
1/242 Sir Fred Schonell Drive St. Lucia QLD 4067Australia e-mail: lermer@mailbox.uq.edu.au
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Abstract

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In this note we investigate lacunarity or ‘thin’ subsets in the dual object of a compact group via different classes of summing operators between Banach spaces. In particular, we give characterisations of Sidon and ∧ (p) sets, 2 < p < ∞

MSC classification

Secondary: 47B10: Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) 42A55: Lacunary series of trigonometric and other functions; Riesz products
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 1 , August 2001 , pp. 71 - 79
Copyright
Copyright © Australian Mathematical Society 2001

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