Weyl’s Theorem for pairs of commuting hyponormal operators

Sameer Chavan; Raúl Curto

doi:10.1090/proc/13479

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Weyl’s Theorem for pairs of commuting hyponormal operators

Journal article

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Weyl’s Theorem for pairs of commuting hyponormal operators

Sameer Chavan and Raúl Curto

Proceedings of the American Mathematical Society, Vol.145(8), pp.3369-3375

08/01/2017

DOI: 10.1090/proc/13479

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Abstract

Let T be a pair of commuting hyponormal operators satisfying the so-called quasitriangular property dim ker (T - lambda) >= dim ker (T - lambda)*, for every lambda in the Taylor spectrum sigma(T) of T. We prove that the Weyl spectrum of T, omega(T), satisfies the identity omega(T) = sigma(T)\pi 00( T), where pi 00(T) denotes the set of isolated eigenvalues of finite multiplicity. Our method of proof relies on a (strictly 2-variable) fact about the topological boundary of the Taylor spectrum; as a result, our proof does not hold for d-tuples of commuting hyponormal operators with d > 2.

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Mathematics, Applied

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Details

Title: Subtitle: Weyl’s Theorem for pairs of commuting hyponormal operators
Creators: Sameer Chavan - Indian Institute of Technology Kanpur
Raúl Curto - University of Iowa, Mathematics
Resource Type: Journal article
Publication Details: Proceedings of the American Mathematical Society, Vol.145(8), pp.3369-3375
DOI: 10.1090/proc/13479
ISSN: 0002-9939
eISSN: 1088-6826
Publisher: American Mathematical Society
Number of pages: 7
Grant note: DMS-1302666 / NSF; National Science Foundation (NSF)
Language: English
Date published: 08/01/2017
Academic Unit: Mathematics
Record Identifier: 9983985920502771

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