This article is cited in 7 papers

Generalized Limits and Related Asymptotic Formulas

A. A. Sedaev

Voronezh State Academy of Building and Architecture

Abstract: On the basis of the new version of Karamata's theorem, stated in terms of generalized limits, we succeed in weakening the conditions of validity of the Connes asymptotic formulas studied by many authors. Using this approach, we can apply the criterion of “measurability” due to Connes for passing from generalized limits to ordinary limits.

Keywords: generalized limit, Dixmier trace, operator ideal, Marcinkiewicz space, Cesàro operator, Karamata theorem, Lebesgue–Stieltjes integral, Hilbert space, dilation operator.

UDC: 517.51

Received: 15.12.2007
Revised: 15.03.2009

DOI: 10.4213/mzm4727

 English version: Mathematical Notes, 2009, 86:4, 577–590

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