Geodesic
Geometric properties of the set of Banach limits
Izvestiya. Mathematics , Tome 78 (2014) no. 3, pp. 596-620.

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We study the geometry and extreme points of the set $\mathfrak B\subset l_\infty^*$ of all positive normalized shift-invariant functionals on the space $l_\infty$ of all bounded sequences with the uniform norm. In particular, we calculate the radius of $\mathfrak B$ and, for a large class of sequences $x$, describe the orbit of $x$ under the extreme points of $\mathfrak B$.
Keywords: Banach limit, extreme point, almost convergent sequence. 
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E. M. Semenov; F. A. Sukochev; A. S. Usachev. Geometric properties of the set of Banach limits. Izvestiya. Mathematics , Tome 78 (2014) no. 3, pp. 596-620. http://geodesic.mathdoc.fr/item/IM2_2014_78_3_a8/

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