Representation of non-semibounded quadratic forms and orthogonal additivity Articles uri icon

publication date

  • September 2018

start page

  • 1

end page

  • 28

International Standard Serial Number (ISSN)

  • WWWW-0074

abstract

  • In this article we give a representation theorem for non-semibounded Hermitean quadratic forms in terms of a (non-semibounded) self-adjoint operator. The main assumptions are closability of the Hermitean quadratic form, the direct integral structure of the underlying Hilbert space and orthogonal additivity. We apply this result to several examples, including the position operator in quantum mechanics and quadratic forms invariant under a unitary representation of a separable locally compact group. The case of invariance under a compact group is also discussed in detail.