What is Nuclear operators between Banach spaces?

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.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 presents both cases but concentrates on the general case of nuclear operators on Banach spaces; for more details about the important special case of nuclear operators on Hilbert space, see the article Trace class.