Abstract:
Let $B$ be a closed dissipative operator in a Hilbert space $H$ with an arbitrary domain of definition. We will give a description of all closed (and, in particular, closed maximal) dissipative extensions $\widetilde B$ of $B$ in terms of extensions $\widetilde W$ of a nonexpanding operator $W$ associated with $B$. We construct a family $\{Â_z\}$ of maximal closed dissipative extensions of $B$, where $z$ is a complex number in the lower half-plane. We present an example which illustrates the above concepts.
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