On a singular part of an unbounded operator
A densely defined linear operator A on a Hilbert space is said to be singular if, for each \(x\in R(A)\), there is a sequence \(y_ n\) in the domain of A such that \(y_ n\to 0\) and \(Ay_ n\to x\). The author gives a number of characterizations of singularity and related results. In particular, it is shown that if two operators are unitarily equivalent, then so are their canonical projections [in the sense of \textit{P. E. T. Jørgensen}, J. Funct. Anal. 39, 281-307 (1980; Zbl 0458.47034)].
scientific article; zbMATH DE number 4073761