The Proper Dissipative Extensions of a Dual Pair
| Autor: | Fischbacher, Christoph, Naboko, Sergey, Wood, Ian |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $A$ and $(-\widetilde{A})$ be dissipative operators on a Hilbert space $\mathcal{H}$ and let $(A,\widetilde{A})$ form a dual pair, i.e. $A\subset\widetilde{A}^*$, resp.\ $\widetilde{A}\subset A^*$. We present a method of determining the proper dissipative extensions $\widehat{A}$ of this dual pair, i.e. $A\subset \widehat{A}\subset\widetilde{A}^*$ provided that $\mathcal{D}(A)\cap\mathcal{D}(\widetilde{A})$ is dense in $\mathcal{H}$. Applications to symmetric operators, symmetric operators perturbed by a relatively bounded dissipative operator and more singular differential operators are discussed. Finally, we investigate the stability of the numerical range of the different dissipative extensions. Comment: 23 pages |
| Databáze: | arXiv |
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