Note on the Kato property of sectorial forms
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Contributors
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
| Original language | English |
|---|---|
| Pages (from-to) | 191-204 |
| Number of pages | 14 |
| Journal | Journal of Operator Theory |
| Volume | 2022 |
| Issue number | 88(1) |
| Publication status | Published - 2022 |
| Peer-reviewed | Yes |
External IDs
| Scopus | 85132573764 |
|---|---|
| WOS | 000907120200008 |
| ORCID | /0000-0002-6854-0586/work/142232357 |
Keywords
DFG Classification of Subject Areas according to Review Boards
ASJC Scopus subject areas
Keywords
- bilinear forms, Sectorial forms, Accretive operators, Kato's square root problem, Kato property