Note on the Kato property of sectorial forms

Research output: Contribution to journalResearch articleContributedpeer-review



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.


Original languageEnglish
Pages (from-to)191-204
Number of pages14
JournalJournal of Operator Theory
Issue number88(1)
Publication statusPublished - 2022

External IDs

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


DFG Classification of Subject Areas according to Review Boards

ASJC Scopus subject areas


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

Library keywords