Geodesic
Haar negligibility of positive cones in Banach spaces
Algebra i analiz, Tome 27 (2015) no. 5, pp. 32-68.

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The Haar negligibility of the positive cone associated with a basic sequence is discussed in the case of a separable Banach space. In particular, it is shown that, up to equivalence, the canonical basis of $c_0$ is the only normalized subsymmetric unconditional basic sequence whose positive cone is not Haar null, and the only normalized unconditional basic sequence whose positive cone contains a translate of every compact set. It is also proved that an unconditional basic sequence with a non-Haar null positive cone must be $c_0$-saturated in a very strong sense, and that every quotient of the space generated by such a sequence is $c_0$-saturated.
Keywords: Haar negligibility, positive cone, Schauder base, Gauss negligibility. 
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J. Esterle; É. Matheron; P. Moreau. Haar negligibility of positive cones in Banach spaces. Algebra i analiz, Tome 27 (2015) no. 5, pp. 32-68. http://geodesic.mathdoc.fr/item/AA_2015_27_5_a1/

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