On products of non-commuting sectorial operators
Frank Weber · French digital mathematics library (Numdam) · 1998
Products of non-commuting sectorial operators are investigated to provide functional-analytical tools for the treatment of multiplicative perturbations and degenerations in evolution problems. Using the operator sum method, combined with the theory of operators with bounded imaginary powers, the following result is shown: If sectorial operators A and B in a Banach space of class ~CT possess bounded imaginary powers, satisfy a parabolicity condition, and fulfil an appropriate commutator estimate, then v + A B is sectorial as well for a sufficiently large v > 0. Examples show that the result can be applied to degenerate parabolic problems.