Extensions of dissipative operators with closable imaginary part
arXiv:2012.12920
Abstract
Given a dissipative operator on a complex Hilbert space such that the quadratic form $f\mapsto \mbox{Im}\langle f,Af\rangle$ is closable, we give a necessary and sufficient condition for an extension of to still be dissipative. As applications, we describe all maximally accretive extensions of strictly positive symmetric operators and all maximally dissipative extensions of a highly singular first-order operator on the interval.
11 pages