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Weyl’s theorem holds for algebraically hyponormal operators. (English) Zbl 0953.47018
It is shown that if \(T\) is an “algebraically hyponormal” operator, i.e., \(p(T)\) is hyponormal for some nonconstant complex polynomial \(p\), then for every \(f\in H(\sigma(T))\), Weyl’s theorem holds for \(f(T)\), where \(H(\sigma(T))\) denotes the set of analytic functions on an open neighborhood of \(\sigma(T)\).

MSC:
47B20 Subnormal operators, hyponormal operators, etc.
47A10 Spectrum, resolvent
47A53 (Semi-) Fredholm operators; index theories
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