Linear Hilbertian manifold domains

TL;DR

This paper characterizes when a dense subspace of a Hilbert space can serve as a linear Hilbertian manifold domain and explores its relation to self-adjoint operator domains.

Contribution

It provides necessary and sufficient conditions for dense subspaces to be linear Hilbertian manifold domains and links these to self-adjoint operator domains.

Findings

Characterization of linear Hilbertian manifold domains

Relations between these domains and self-adjoint operator domains

Conditions for a subspace to be a Hilbertian manifold domain

Abstract

Necessary and sufficient conditions for a dense subspace of a Hilbert space to be a linear Hilbertian manifold domain are given. Some relations between linear Hilbertian manifold domains and domains of self-adjoint operators are found.