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Putnam’s theorems for \(w\)-hyponormal operators. (English) Zbl 0976.47017

Summary: Three theorems on hyponormal operators due to Putnam are generalized to apply to the broader class of \(w\)-hyponormal operators. In particular, it is shown that if an operator \(T\) is \(w\)-hyponormal and the spectrum of \(|T^*|\) is not an interval, then \(T\) has a nontrivial invariant subspace.

MSC:

47B20 Subnormal operators, hyponormal operators, etc.
47A10 Spectrum, resolvent
47A15 Invariant subspaces of linear operators
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