Abstract

As a consequence of the exposition of Dixmier type traces in the book of A. Connes (1994) [2], we were led to ask how general is this class of functionals within the space of all unitarily invariant functionals on the corresponding Marcinkiewicz ideal M ψ . In this paper we prove the surprising result that the set of all Dixmier traces on M ψ coincides with the set of all fully symmetric functionals on this space.

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