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.[1] The theorem was proven in 1955 by Alexander Grothendieck.[2] 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.
^Gohberg, Israel; Goldberg, Seymour; Krupnik, Nahum (1991). Traces and Determinants of Linear Operators. Operator Theory Advances and Applications. Basel: Birkhäuser. p. 102. ISBN 978-3-7643-6177-8.
^* Grothendieck, Alexander (1955). Produits tensoriels topologiques et espaces nucléaires (in French). Providence: American Mathematical Society. p. 19. ISBN 0-8218-1216-5. OCLC 1315788.
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