Note on the Kato property of sectorial forms

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

We characterise the Kato property of a sectorial form a, defined on a Hilbert space V, with respect to a larger Hilbert space H in terms of two bounded, selfadjoint operators T and Q determined by the imaginary part of a and the embedding of V into H, respectively. As a consequence, we show that if a bounded selfadjoint operator T on a Hilbert space V is in the Schatten class S p(V) (p ≥ 1), then the associated form (Formula Presented) has the Kato property with respect to every Hilbert space H into which V is densely and continuously embedded. This result is in a sense sharp. Another result says that if T and Q commute then the form a with respect to H possesses the Kato property.

Details

OriginalspracheEnglisch
Seiten (von - bis)191-204
Seitenumfang14
FachzeitschriftJournal of Operator Theory
Jahrgang88
Ausgabenummer1
PublikationsstatusVeröffentlicht - 2022
Peer-Review-StatusJa

Externe IDs

Scopus 85132573764
WOS 000907120200008
ORCID /0000-0002-6854-0586/work/142232357

Schlagworte

DFG-Fachsystematik nach Fachkollegium

ASJC Scopus Sachgebiete

Schlagwörter

  • bilinear forms, Sectorial forms, Accretive operators, Kato's square root problem, Kato property