On unbounded hyponormal operators (Q1825425)

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.