Essentially coercive forms and asymptotically compact semigroups

[摘要] Form methods are most efficient to prove generation theorems for semigroups but also for proving selfadjointness. So far those theorems are based on a coercivity notion which allows the use of the Lax-Milgram Lemma. Here we consider weaker essential versions of coerciveness which already suffice to obtain the generator of a semigroup S or a selfadjoint operator. We also show that one of these properties, namely essentially positive coerciveness implies a very special asymptotic behaviour of S, namely asymptotic compactness; i.e. that dist(S(t), K(H)) -> 0 as t -> infinity where K(H) denotes the space of all compact operators on the underlying Hilbert space. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-11-15

[关键词] Sesquilinear coercive forms;Essentially coercive forms;Elliptic forms;Numerical range;Selfadjoint operators;Asymptotically compact semigroups