A nuclear operator between Banach spaces 
and 
is a bounded linear operator 
admitting a representation
 |
with 
,
, and 
. Every nuclear operator is compact. On a Hilbert
space, nuclear operators coincide with trace-class operators.
Nuclear Operator
See also
Banach Space, Compact Operator, Trace-Class OperatorExplore with Wolfram|Alpha
References
Pietsch, A. Operator Ideals. Amsterdam, Netherlands: North-Holland, 1980.Cite this as:
Weisstein, Eric W. "Nuclear Operator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NuclearOperator.html