In functional analysis, the Grothendieck trace theorem is an extension of Lidskii's theorem about the trace and the determinant of a certain class of nuclear operators on Banach spaces, the so-called -nuclear operators. The theorem was proven in 1966 by Alexander Grothendieck. Lidskii's theorem does not hold in general for Banach spaces. The theorem should not be confused with the Grothendieck trace formula from algebraic geometry. Grothendieck trace theorem Given a Banach space with the approximation property and denote its dual as . -nuclear operators Let be a nuclear operator on , then is a -nuclear operator if it has a decomposition of the form where and and Grothendiecks trace theorem Let denote the eigenvalues of counted with their algebraic multiplicities. If then the following equalities hold: and for the Fredholm determinant See also Literature References Functional analysis Topological tensor products