In mathematics, a nuclear operator is a compact operator for which a trace may be defined, such that the trace is finite and independent of the choice of basis (at least on well behaved spaces; there are some spaces on which nuclear operators do not have a trace). Nuclear operators are essentially the same as trace class operators, though most authors reserve the term "trace class operator" for the special case of nuclear operators on Hilbert spaces. The general definition for Banach spaces was given by Grothendieck. This article concentrates on the general case of nuclear operators on Banach spaces; for the important special case of nuclear (=trace class) operators on Hilbert space see the article on trace class operators.
Read more about Nuclear Operator: Compact Operator, Nuclear Operator, Properties, On Banach Spaces
Famous quotes containing the word nuclear:
“You can’t be a Real Country unless you have A BEER and an airline—it helps if you have some kind of a football team, or some nuclear weapons, but at the very least you need a BEER.”
—Frank Zappa (1940–1993)