Domination of semigroups on standard forms of von Neumann algebras

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

Consider (Tt)t≥0 and (St)t≥0 as real C -semigroups generated by closed and symmetric sesquilinear forms on a standard form of a von Neumann algebra. We provide a characterisation for the domination of the semigroup (Tt)t≥0 by (St)t≥0 , which means that - Stv≤ Ttu≤ Stv holds for all t≥ 0 and all real u and v that satisfy - v≤ u≤ v . This characterisation extends the Ouhabaz characterisation for semigroup domination to the non-commutative L2 -spaces. Additionally, we present a simpler characterisation when both semigroups are positive as well as consider the setting in which (Tt)t≥0 need not be real.

Details

OriginalspracheEnglisch
Seiten (von - bis)715-729
Seitenumfang15
FachzeitschriftArchiv der Mathematik
Jahrgang121
Ausgabenummer5-6
PublikationsstatusVeröffentlicht - Nov. 2023
Peer-Review-StatusJa

Externe IDs

ORCID /0000-0002-6854-0586/work/148603583
Scopus 85177881129

Schlagworte

Schlagwörter

  • Domination of semigroups, Noncommutative theory, Quadratic forms, Standard forms of von Neumann algebras