Geodesic
On the A.\,M.~Bikchentaev conjecture
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2012), pp. 67-70

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In 1998 A. M. Bikchentaev conjectured that for positive $\tau$-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.
Keywords: von Neumann algebra, normal trace, $\tau$-measurable operator, Hardy–Littlewood submajorization, Golden–Thompson inequality, singular trace. 
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     author = {F. A. Sukochev},
     title = {On the {A.\,M.~Bikchentaev} conjecture},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {67--70},
     publisher = {mathdoc},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_6_a7/}
}
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F. A. Sukochev. On the A.\,M.~Bikchentaev conjecture. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2012), pp. 67-70. http://geodesic.mathdoc.fr/item/IVM_2012_6_a7/