It is well known that RN has subspaces of dimension proportional to N on which the l1 norm is equivalent to the l2 norm; however, no explicit constructions are known. Extending earlier work by Artstein– Avidan and Milman, we prove that such a subspace can be generated using O(N) random bits.

We prove an isoperimetric inequality for uniformly log-concave measures and for the uniform measure on a uniformly convex body. These inequalities imply the log-Sobolev inequalities proved by Bobkov and Ledoux [12] and Bobkov and Zegarlinski [13]. We also recover a concentration inequality for uniformly convex bodies, similar to that proved by Gromov and Milman [22].

The goal of this note is to introduce new classes of operator ideals, and, moreover, a new way of constructing such classes through an application to operators of the asymptotic structure recently introduced by Maurey, Milman, and Tomczak-Jaegermann in Op. Th. Adv. Appl. 77 (1995), 149–175.

We give conditions for the Mayer-Vietoris property to hold for the algebraic K-theory of blow-up squares of toric varieties and schemes, using the theory of monoid schemes. These conditions are used to relate algebraic K-theory to topological cyclic homology in characteristic p. To achieve our goals, we develop many notions for monoid schemes based on classical algebraic geometry, such as separ...

We initiate the study of matrix convexity for operator spaces. define notion compact rectangular convex set, and prove natural analogs Krein-Milman bipolar theorems in this context. deduce a canonical correspondence between sets also introduce boundary representation an space, analog Arveson's conjecture: every space is completely normed by its representations. This yields construction triple e...