On unbounded subnormal operators
An operator S with a dense domain D(S) in a Hilbert space H is called subnormal if there exists a normal operator N with a dense domain D(N) in a Hilbert space K such that \(H\subset K\), D(S)\(\subseteq D(N)\) and \(Nx=Sx\) for all \(x\in D(S)\). It is shown that some well-known theorems of bounded case remain valid for unbounded subnormal operators. Here are some instances. (i) Every subnormal operator admits a minimal normal extension. (ii) If \(\{N^{*j}N^ ix:\) \(x\in \cap^{\infty}_{1}D(S^ n)\), \(i,j=1,2,...\}\) is dense in K, then N is a minimal normal extension. (iii) If N is a minimal normal extension of S, then \(\sigma\) (N)\(\subseteq \sigma (S).\) The paper also contains some results which are particular to the unbounded case.
scientific article; zbMATH DE number 4109405
scientific article