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Fully symmetric functionals on a Marcinkiewicz space are Dixmier traces |
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| Authors: | NJ Kalton AA Sedaev FA Sukochev |
| Institution: | aDepartment of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA;bDepartment of Mathematics, Voronezh State University of Architecture and Construction, 20-letiya Oktyabrya 84, Voronezh 394006, Russia;cSchool of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia |
| 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 Mψ. In this paper we prove the surprising result that the set of all Dixmier traces on Mψ coincides with the set of all fully symmetric functionals on this space. |
| Keywords: | MSC: 47B10 46A22 |
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