Quadratic operators and invariant subspaces
Quasiaffine transforms of operators
We obtain a new sufficient condition (which may be useful elsewhere) that a compact perturbation of a normal operator be the quasiaffine transform of some normal operator. We also give some applications of this result.
Quasi-invariant subspaces generated by polynomials with nonzero leading terms
We introduce a partial order relation in the Fock space. Applying it we show that for the quasi-invariant subspace [p] generated by a polynomial p with nonzero leading term, a quasi-invariant subspace M is similar to [p] if and only if there exists a polynomial q with the same leading term as p such that M = [q].
Quasireducible operators.