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:
“Take pains ... to write a neat round, plain hand, and you will find it a great convenience through life to write a small and compact hand as well as a fair and legible one.”
—Thomas Jefferson (1743–1826)