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.
Read more about this topic: Nuclear Operator
Famous quotes containing the word compact:
“The powers of the federal government ... result from the compact to which the states are parties, [and are] limited by the plain sense and intention of the instrument constituting that compact.”
—James Madison (1751–1836)