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Singular Traces and Compact Operators

โœ Scribed by S Albeverio; D Guido; A Ponosov; S Scarlatti

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
922 KB
Volume
137
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

We give a necessary and sufficient condition on a positive compact operator T for the existence of a singular trace (i.e. a trace vanishing on the finite rank operators) which takes a finite non-zero value on T. This generalizes previous results by Dixmier and Varga. We also give an explicit description of these traces and associated ergodic states on l (N) using tools of non standard analysis in an essential way.

๐Ÿ“œ SIMILAR VOLUMES

Singular Values of Compact Pseudodiffere
Singular Values of Compact Pseudodifferential Operators
โœ C Heil; J Ramanathan; P Topiwala ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 420 KB

This paper investigates the asymptotic decay of the singular values of compact operators arising from the Weyl correspondence. The motivating problem is to find sufficient conditions on a symbol which ensure that the corresponding operator has singular values with a prescribed rate of decay. The pro