Source: wikibot/silverman-toeplitz-theorem
= Silverman–Toeplitz theorem
{wiki=Silverman–Toeplitz_theorem}
The Silverman-Toeplitz theorem is a result in functional analysis and operator theory concerning the convergence of certain types of series of bounded linear operators. Specifically, it addresses the behavior of a series of projections in a Hilbert space. The theorem can be stated as follows: Let \\( H \\) be a Hilbert space and let \\( \\\{ P_n \\\} \\) be a sequence of orthogonal projections in \\( H \\).