nLab
separable Hilbert space

Contents

Definition

A Hilbert space H over a field F of real or complex numbers and with inner product () is separable if it has a countable topological base, i. e. a family of vectors e i, iI where I is at most countable, and such that every vector vH can be uniquely represented as a series v= iIa ie i where a iF and the sum converges in the norm x=(xx).

Revised on April 5, 2013 17:10:46 by Urs Schreiber (131.174.41.18)