One criterion of semigroup product convergence

✍ Scribed by A. G. Beliy; Yu. A. Semenov

• Book ID: 104766894
• Publisher: Springer
• Year: 1976
• Tongue: English
• Weight: 418 KB
• Volume: 1
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00417604

✦ Synopsis

Let exp(-tA) and exp(-tB) be Co contraction semigroups on both ~f and ~, where Jr'is a Hilbert space and ~ is a reflexive Banach space such that the linear space ~N~ is dense both in Js and ~. Let ~*CJfC,~, (~, ~*) be a dual pair of Banach spaces. In this paper we study some properties of inf'mitesimal operators of these semigroups. We show that under suitable assumptions there is some connection between the form-sum A~-B and a closure ofA, +B1, where -.41 is an infinitesimal operator of Co contraction semigroup exp(-tA 1 ) which is the extension by continuity on ~ of Co contraction semigroup exp(-tA)~ ~c'~f in ,~. In particular we give some criterion of an m-accretive closability A ~ +B~ which may be applied for example to the Schrfdinger operators acting in suitable L p-spaces. Also this criterion together with &Contraction properties of semigroups under consideration results in the establishment of the Lie-Trotter formulae.