The trace formula in Banach spaces

W. B. Johnson*, A. Szankowski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

A classical result of Grothendieck and Lidskii says that the trace formula (that the trace of a nuclear operator is the sum of its eigenvalues provided the sequence of eigenvalues is absolutely summable) holds in Hilbert spaces. In 1988, Pisier proved that weak Hilbert spaces satisfy the trace formula. We exhibit a much larger class of Banach spaces, called Γ-spaces, that satisfy the trace formula. A natural class of asymptotically Hilbertian spaces, including some spaces that are ℓ2 sums of finite-dimensional spaces, are Γ-spaces. One consequence is that the direct sum of two Γ-spaces need not be a Γ-space.

Original languageEnglish
Pages (from-to)389-404
Number of pages16
JournalIsrael Journal of Mathematics
Volume203
Issue number1
DOIs
StatePublished - Oct 2014

Bibliographical note

Publisher Copyright:
© 2014, Hebrew University of Jerusalem.

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