Maximal nonnegative and $\theta$-accretive extensions of a positive definite linear relation

Abstract

Let $L_{0}$ be a closed linear positive definite relation ("multivalued operator") in a complex Hilbert space. Using the methods of the extension theory of linear transformations in a Hilbert space, in the terms of so called boundary value spaces (boundary triplets), i.e. in the form that in the case of differential operators leads immediately to boundary conditions, the general forms of a maximal nonnegative, and of a proper maximal $\theta$-accretive extension of the initial relation $L_{0}$ are established.