Measures on the Closed Subspaces of a Hilbert Space

Abstract

In his investigations of the mathematical foundations of quantum mechanics, Mackey¹ has proposed the following problem: Determine all measures on the closed subspaces of a Hilbert space. A measure on the closed subspaces means a function μ which assigns to every closed subspace a non-negative real number such that if {A _i} is a countable collection of mutually orthogonal subspaces having closed linear span B, then

$$ \mu (B) = \sum {\mu \left( {{A_i}} \right)} $$

.

Keywords

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The author has been partially supported by the Office of Ordnance Research, Contract No. DA 19-020-ORD-3778. He is indebted also to R. V. Kadison for helpful remarks.