Perturbations of linear 𝑚-accretive operations

Abstract

Abstract.A sufficient condition is given for the sum A+B of two linear /«-accretive operators A and B in a Hubert space to be /72-accretive. This condition is expressed in terms of Re(/4«, Bu) for u in D, where D is a certain linear manifold contained in D(A+B).

On the solvability of fourth-order boundary value problems with accretive operators

“…By Theorem 2 in [10] we deduce that B 2 + C − γI is m-accretive. Also (3.10) implies (3.9) in the case of δ = 0, see [20], Remark 4.4. Thus the assumption (3.9) is stronger than the relative boundedness.…”

“…Such results are interesting, firstly because they provide an existence, uniqueness and L p -maximal regularity of the solution for the fourth order abstract boundary value problem (1.1) under some necessary and sufficient conditions on the data. Moreover, they are of interest regarded as an application of the perturbation theory of m-accretive operators, [10], [11], [13], [20], [21], [22], [32]. This allows us to find various sufficient conditions on the accretive operators B and C, under which our results remains valid.…”