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The spectral boundary of complemented invariant subspaces in Lp(R)

Published online by Cambridge University Press:  12 July 2007

Zoltán Buczolich  and
Alexander Olevskiĭ
Zoltán Buczolich
Affiliation:
Department of Analysis, Eötvös Loránd University, Budapest, Kecskeméti u. 10-12, H-1053, Hungary (buczo@ludens.elte.hu)
Alexander Olevskiĭ
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv 69978, Israel (olevskii@math.tau.ac.il)
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Abstract

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In this paper we construct a compact set K of zero Hausdorff dimension that satisfies certain ‘arithmetic-type’ thickness properties. The concept of ‘arithmetic thickness’ has its origins in applications to harmonic analysis, introduced in a paper by Lebedev and Olevskiĭ. For example, there are no spectral sets whose ‘essential boundary’ can contain the above set K.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 4 , August 2001 , pp. 785 - 798
Copyright
Copyright © Royal Society of Edinburgh 2001