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On the geometry of proportional quotients of l m

Piotr MankiewiczStanisław J. Szarek — 2003

Studia Mathematica

We compare various constructions of random proportional quotients of l m (i.e., with the dimension of the quotient roughly equal to a fixed proportion of m as m → ∞) and show that several of those constructions are equivalent. As a consequence of our approach we conclude that the most natural “geometric” models possess a number of asymptotically extremal properties, some of which were hitherto not known for any model.

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