Local spectrum and subharmonicity

Local spectrum and subharmonicity

Introducing the technique of subharmonic functions, we prove that the local spectrum Spu(λ)(T) is almost constant if u is an analytic family of vectors and if the spectrum of T is thin, a result which is similar to the finite-dimensional situation. We apply this result to improve a former result of...

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Veröffentlicht in:Proceedings of the Edinburgh Mathematical Society 1996-10, Vol.39 (3), p.571-579
Hauptverfasser: Aupetit, B., Drissi, D.
Format: Artikel
Sprache:eng
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Zusammenfassung:Introducing the technique of subharmonic functions, we prove that the local spectrum Spu(λ)(T) is almost constant if u is an analytic family of vectors and if the spectrum of T is thin, a result which is similar to the finite-dimensional situation. We apply this result to improve a former result of C. Foiaş [7] on generalized scalar operators and results of C. Foiaş and F. -H. Vasilescu [8] on generalized commutators.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091500023312