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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     author = {E. M. Semenov and F. A. Sukochev and A. S. Usachev},
     title = {Geometric properties of the set of {Banach} limits},
     journal = {Izvestiya. Mathematics },
     pages = {596--620},
     publisher = {mathdoc},
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     number = {3},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2014_78_3_a8/}
}
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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/