 Beurling–Lax theorem

The Beurling–Lax theorem is an important result in the field of functional analysis, specifically in the study of linear operators and the theory of semi-groups. It establishes a link between the spectrum of a bounded linear operator on a Banach space and its invariant subspaces, particularly in the context of unitary operators. More specifically, the theorem is often stated in relation to one-dimensional cases and can be understood in terms of the spectral properties of a self-adjoint operator.