Nuclear Operator - Compact Operator

Compact Operator

An operator on a Hilbert space

is said to be a compact operator if it can be written in the form

where and and are (not necessarily complete) orthonormal sets. Here, are a set of real numbers, the singular values of the operator, obeying if . The bracket is the scalar product on the Hilbert space; the sum on the right hand side must converge in norm.