On a class on nondensely defined contractions and their extensions (Q1971742)

Let \(H\) be a complex Hilbert space, \(\alpha\in (0,\pi/2]\) and \(I\) the identity operator in \(H\). If a linear operator \(A: D(A)\subset H\to H\) satisfies \(\|\sin\alpha A\pm i\cos\alpha I\|\leq 1\), then, in case \(D(A)= H\), we say that \(A\) belongs to the class \(C(\alpha)\) and in the case \(D(A)\neq H\) the operator \(A\) is a \(C(\alpha)\)-suboperator. The paper deals with the following general problem: if \(A\) is a \(C(\alpha)\)-suboperator with \(\alpha\in [0,\pi/2)\), describe all extensions of class \(C(\beta)\) of this operator, for \(\beta\in [\alpha,\pi/2]\).