In:
Journal of Operator Theory, Theta Foundation, Vol. 88, No. 1 ( 2022-07-15), p. 191-204
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 Sp(V) (p⩾1), then the associated form aT(⋅,⋅):=⟨(I+iT)⋅,⋅⟩V 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.
Type of Medium:
Online Resource
ISSN:
0379-4024
,
1841-7744
DOI:
10.7900/jot.y2022v088i01
DOI:
10.7900/jot.2021jan21.2309
Language:
Unknown
Publisher:
Theta Foundation
Publication Date:
2022
detail.hit.zdb_id:
2043904-0
SSG:
17,1
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