Estimates in operator classes for a difference of functions, from the pick class, of accretive operators

Abstract

was obtained, where o is an arbitrary symmetrically-normed (s.n.) ideal [3] possessing the domination property*. Furthermore, in [21 estimates in the quasi-normed classes of power decrease of the s-numbers were obtained. The results of [I, 2] have been extended by the present author [4] to the case of two maximal dissipative (accretive) operators. Recall that a densely defined operator L in H is called maximal accretive (m.a.o.) [5] if Re (Lh, h) ~ 0 V h ~ (L) and the left half-plane Re ~ < 0 consists entirely of regular points of the operator L. Since an arbitrary maximal dissipative operator [5] is distinguished from a maximal accretive operator only by the multiplier (i), analogous results will be valid for a pair of maximal dissipative operators as well. The choice of the accretive case is motivated only by some notational convenience.