Note on the Kato property of sectorial forms
| Autor: | Chill, Ralph, Krol, Sebastian |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We characterise the Kato property of a sectorial form $\mathfrak{a}$, 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 $\mathfrak{a}$ 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 $S_p(V)$ ($p\geq 1$), then the associated form $\mathfrak{a}_T(\cdot, \cdot) := \langle (I+iT)\cdot ,\cdot\rangle_V$ 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 $\mathfrak{a}$ with respect to $H$ possesses the Kato property. Comment: 12 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|