Journal of Operator Theory

Volume 92, Issue 1, Summer 2024 pp. 3-24.

M-accretive realisations of skew-symmetric operators

Authors: Rainer Picard (1), Sascha Trostorff (2)
Author institution:(1) Fakultaet fuer Mathematik, TU Dresden, Dresden, 01062, Germany
(2) Mathematisches Seminar, CAU Kiel, Kiel, 24098, Germany

Summary: We consider skew-symmetric operators $A_{0}$ on a Hilbert space $H$ and characterise all (nonlinear) m-accretive restrictions of $A:=-A_{0}^{\ast}$ in terms of the ``deficiency spaces'' $\ker(1\pm A)$. The results are illustrated by several examples and applied to a partial differential equation with an impedance type boundary condition.

DOI: http://dx.doi.org/10.7900/jot.2022jul12.2401
Keywords: M-accretive and skew-symmetric operators, deficiency spaces, block-operator matrices, boundary conditions of impedance type

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