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On the A. M. Bikchentaev conjecture

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Abstract

In 1998 A. M. Bikchentaev conjectured that for positive τ-measurable operators a and b affiliated with a semifinite von Neumann algebra, the operator b 1/2 ab 1/2 is submajorized by the operator ab in the sense of Hardy-Littlewood. We prove this conjecture in its full generality and obtain a number of consequences for operator ideals, Golden-Thompson inequalities, and singular traces.

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Authors and Affiliations

  1. University of New South Wales, Sydney, NSW, 2052, Australia

    F. A. Sukochev

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  1. F. A. Sukochev
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Correspondence to F. A. Sukochev.

Additional information

Original Russian Text © F.A. Sukochev, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 6, pp. 67–70.

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Sukochev, F.A. On the A. M. Bikchentaev conjecture. Russ Math. 56, 57–59 (2012). https://doi.org/10.3103/S1066369X12060084

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  • DOI: https://doi.org/10.3103/S1066369X12060084

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