On one generalization of the Berezanskii evolution criterion for the self-adjointness of operators - Gorbachuk, V. I.; Gorbachuk, M. L. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
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.