325 research outputs found
On a conjecture of A. Bikchentaev
In \cite{bik1}, A. M. Bikchentaev conjectured that for positive
measurable operators and affiliated with an arbitrary semifinite
von Neumann algebra , the operator is
submajorized by the operator in the sense of Hardy-Littlewood. We prove
this conjecture in full generality and present a number of applications to
fully symmetric operator ideals, Golden-Thompson inequality and (singular)
traces.Comment: "Spectral Analysis, Differential Equations and Mathematical Physics",
H. Holden et al. (eds), Proceedings of Symposia in Pure Mathematics {\bf 87},
Amer. Math. Soc. (to appear
Orbits in symmetric spaces
We characterize those elements in a fully symmetric spaces on the interval
or on the semi-axis whose orbits are the norm-closed
convex hull of their extreme points. Our results extend and complement earlier
work on the same theme by Braverman and Mekler
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