One example of a quasihyperbolic operator pencil (Q1096867)

The operator pencil \(L(Z)=Z\) \(2+BZ+C\) is quasihyperbolic, if C,B are bounded operators, \(C>0\), \(B>0\) and C, \(B^{-1}\) \(C^{1/2}\) are compact operators. In this article an example of quasi-hyperbolic pencil is constructed, for which the root of a quadratic operator equation \[ Z^ 2+BZ+C=0 \] has the form \[ Z=KC^{1/2}, \] where K is noncompact.