A generalization of Stenger’s lemma to maximal dissipative operators. (English) Zbl 1248.47037
Let the Hilbert space \({\mathcal H}\) be the orthogonal sum \({\mathcal H=\mathcal F\oplus \mathcal G}\) of two Hilbert spaces \({\mathcal F, \mathcal G}\) with \({\text{dim}\;{\mathcal G} < \infty}\). Let \(P_{\mathcal F}\) denote the orthogonal projection in \({\mathcal H}\) onto \({\mathcal F}\).
It is shown that, for any maximal dissipative operator \(A\), the operator \(P_{\mathcal F} A|_{ \text{dom} A\cap\mathcal F}\) is again a maximal dissipative operator in \(\mathcal F\).
It is shown that, for any maximal dissipative operator \(A\), the operator \(P_{\mathcal F} A|_{ \text{dom} A\cap\mathcal F}\) is again a maximal dissipative operator in \(\mathcal F\).
Reviewer: Michael Perelmuter (Kyïv)
MSC:
| 47B44 | Linear accretive operators, dissipative operators, etc. |
| 47A48 | Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. |
References:
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