APPLICATIONS OF MAXIMALITY IN THE DECOMPOSITION OF HILBERT SPACES

The Closed subsets of Hilbert spaces have usually a basic role in the theory of these topological vector spaces. In this talk we introduce a kind of closed subsets D Í H Å H for any Hilbert space H, which has also a kind of maximality and for which every h ϵ H has a unique representation h = x−y for some (x, y) ϵ D. As a consequence, we prove the standard representation of the Hilbert space H as the direct sum of the closure of M and its orthogonal complement for any subspace M Í H. We also discuss some applications.

کلیدواژه ها:

Hilbert spaces ، maximally isotropic ، uniqueness theorem