Dixmier measurability in Marcinkiewicz spaces and applications |
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| Authors: | A.A. Sedaev F.A. Sukochev |
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| Affiliation: | 1. Department of Mathematics, Voronezh State University of Architecture and Civil Engineering, 20-letiya Oktyabrya 84, Voronezh 394006, Russia;2. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia |
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| Abstract: | We present new results concerning the description of Dixmier measurable elements in the sense of A. Connes in Marcinkiewicz spaces and demonstrate some applications of our results. In particular, we complement famous Connes Trace Theorem by describing the asymptotics of the singular function of order −n classical pseudo-differential operators on an n-dimensional compact Riemannian manifold. |
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| Keywords: | Dixmier traces Marcinkiewicz operator ideals |
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