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THE GENERIC LOCAL SPECTRUM OF ANY OPERATOR IS THE FULL SPECTRUM

Published online by Cambridge University Press:  01 May 1999

BEBE PRUNARU  and
MIHAI PUTINAR
BEBE PRUNARU
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA Institute of Mathematics, Romanian Academy, PO Box 1-764, 70700 Bucharest, Romania
MIHAI PUTINAR
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
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Abstract

Let T=(T1, …, Tn) be a commuting n-tuple of bounded linear operators acting on some complex Banach space [Xscr ]. We show that if T has the single-valued extension property, then the local spectrum σT(x) coincides with the spectrum σ(T), for all vectors x∈[Xscr ], except on a set of the first Baire category.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 3 , May 1999 , pp. 332 - 336
Copyright
© The London Mathematical Society 1999

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