On unbounded hyponormal operators. (English) Zbl 0684.47020

A (not necessarily bounded) linear operator T on a Hilbert space is called hyponormal, if \({\mathcal D}(T)\subset {\mathcal D}(T^*)\) and \(\| T^*x\| \leq \| Tx\|\) for \(x\in {\mathcal D}(T)\). After the statement of elementary properties hyponormal operators with spectrum contained in an angle are studied with respect to the generated semigroups and accretivity. For some differential operators and for composition operators in \(L^ 2(\mu)\) conditions implying hyponormality are given.
Reviewer: G.Garske


47B20 Subnormal operators, hyponormal operators, etc.
47D03 Groups and semigroups of linear operators
47E05 General theory of ordinary differential operators
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