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Ukrainian Mathematical Journal

, Volume 52, Issue 5, pp 694–702 | Cite as

On one generalization of the Berezanskii evolution criterion for the self-adjointness of operators

  • M. L. Gorbachuk
  • V. I. Gorbachuk
Article

Abstract

We describe all weak solutions of a first-order differential equation in a Banach space on (0, ∞) and investigate their behavior in the neighborhood of zero. We use the results obtained to establish necessary and sufficient conditions for the essential maximal dissipativity of a dissipative operator in a Hilbert space.

Keywords

Weak Solution Cauchy Problem Vector Function Strong Solution Reflexive Banach Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • M. L. Gorbachuk
    • 1
  • V. I. Gorbachuk
    • 1
  1. 1.Institute of MathematicsUkranian Academy of SciencesKiev

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