Nuclear operators between Banach spaces: Difference between revisions

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In [[mathematics]], a '''nuclear operatoroperators between Banach spaces''' isare a [[linear operator]]s between [[Banach space]]s in infinite dimensions that share some of the properties of their counter-part in finite dimension. In [[Hilbert space]]]s such operators are usually called [[trace class|trace class operators]] and one can define such things as the [[trace (linear algebra)|trace]]. In Banach spaces this is no longer possible for general nuclear operators, it is however possible for <math>\tfrac{2}{3}</math>-nuclear operator via the [[Grothendieck trace theorem]].

The general definition for [[Banach space]]s was given by [[Grothendieck]]. This article presents both cases but concentrates on the general case of nuclear operators on Banach spaces.

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[[Category:Operator theory]]

[[Category:Topological tensor products]]

[[Category:Linear operators]]