This article is cited in 1 paper

Extensions and generalized resolvents of closed dissipative operators

V. I. Utkin

Chuvash Pedagogical Institute

Abstract: Let $B$ be a closed dissipative operator in a Hilbert space $\mathscr H$ with an arbitrary domain of definition. We investigate briefly the problem of describing all the closed (and, in particular, the closed maximal) dissipative extensions $\widetilde B$ of the operator $B$. Following this we introduce the concept of a generalized resolvent of a closed dissipative operator with an arbitrary domain of definition, and we study the fundamental properties of generalized resolvents.

UDC: 513.88

Received: 24.09.1973

 English version: Mathematical Notes, 1974, 16:1, 655–660

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