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Local spectrum and subharmonicity
Published online by Cambridge University Press: 20 January 2009
Abstract
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.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 3 , October 1996 , pp. 571 - 579
- Copyright
- Copyright © Edinburgh Mathematical Society 1996
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