Quasi-self-adjoint contracting dilations of a Hermitian contraction (Q916062)

Suppose A is a Hermitian compression on Hilbert space H with the domain \(D_ A\). A bounded linear operator T on H is said to be a quasi- selfadjoint compressing extension (abb. qsc-extension) of A, if \(T\supset A\), \(T^*\supset A\) and \(\| T\| \leq 1\). Furthermore T is referred to the class C(\(\alpha\)) (\(\alpha\in [0,\pi /2])\), if \(\| \sin \alpha \cdot T\pm i \cos \alpha \cdot I\| \leq 1.\) In this paper the parametric representation and description of all canonical resolutions for the class C(\(\alpha\)) (\(\alpha\in [0,\pi /2])\) is given.