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Extensions of closed dissipative operators

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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\(\tilde B\) of B in terms of extensions\(\tilde W\) of a nonexpanding operator W associated with B. We construct a family {Bz} 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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Authors and Affiliations

  1. Ul'yanov State Pedagogical Institute, USSR

    V. I. Utkin

Authors
  1. V. I. Utkin
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Additional information

Translated from Matematicheskie zametki, Vol. 14, No. 2, pp. 223–232, August, 1973.

The author wishes to thank A. V. Shtraus for his constant attention to this work.

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Utkin, V.I. Extensions of closed dissipative operators. Mathematical Notes of the Academy of Sciences of the USSR 14, 687–691 (1973). https://doi.org/10.1007/BF01147115

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  • DOI: https://doi.org/10.1007/BF01147115

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