Diagana, Toka Fractional powers of hyponormal operators of Putnam type. (English) Zbl 1096.47026 Int. J. Math. Math. Sci. 2005, No. 12, 1925-1932 (2005). Compared to the theory of bounded hyponormal operators, very little is known about unbounded ones. The present note delivers a welcome contribution in this direction. Let \(K\) be a self-adjoint, possibly unbounded operator and let \(L\) be a bounded self-adjoint operator. Then \(A=K+iL\) is hyponormal if \[ \| A^\ast x \| \leq \| Ax \| , \;x \in \text{Dom}(A). \]Note that \(\text{Dom}(A) = \text{Dom}(A^\ast)\) in this case. The author considers two such hyponormal operators \(A\) and \(B\) and the delicate question of estimating the domains of the closures of \((A+B)^\alpha\) and \((A+B)^{\ast \alpha}\), where \(0<\alpha<1\). This is done under some sectoriality assumptions. The main result can be considered as a variation on Kato’s square root problem. An application is included at the end of the note: a non-symmetric, relatively bounded, sectorial perturbation \(T\) of the Schrödinger operator on the whole space \(\mathbb R^d\). An accurate computation of the domains of the fractional powers \(T^\alpha\) is sketched. Reviewer: Mihai Putinar (Santa Barbara) Cited in 1 Document MSC: 47B20 Subnormal operators, hyponormal operators, etc. 47B25 Linear symmetric and selfadjoint operators (unbounded) Keywords:hyponormal operator; sectorial operator; Schrödinger operator; unbounded hyponormal operators; Kato square root problem; fractional powers PDFBibTeX XMLCite \textit{T. Diagana}, Int. J. Math. Math. Sci. 2005, No. 12, 1925--1932 (2005; Zbl 1096.47026) Full Text: DOI EuDML