A direct approach is used to establish both Ball and Barthe’s reverse isoperimetric inequalities for the unit balls of subspaces of Lp. This approach has the advantage that it completely settles all the open uniqueness questions for these inequalities. Affine isoperimetric inequalities generally have ellipsoids as extremals. The so called reverse affine isoperimetric inequalities usually have s...

We show that a reflexive subspace of the predual of a von Neumann algebra embeds into a noncommutative Lp space for some p > 1. This is a noncommutative version of Rosenthal’s result for commutative Lp spaces. Similarly for 1 ≤ q < 2, an infinite dimensional subspace X of a noncommutative Lq space either contains lq or embeds in Lp for some q < p < 2. The novelty in the noncommutative setting i...

Abstract: We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric outliers. We study the recovery of the global l0 subspace (i.e., with largest number of points) by minimizing the lp-averaged distances of data points from d-dimensional subspaces of R , where 0 < p ∈ R. Unlike other lp minimization problems, this minimization is non-convex for all p > 0...

In this article, we consider pair frames in Banach spaces and   introduce Banach pair frames. Some various concepts in the frame theory such as frames, Schauder frames, Banach frames and atomic decompositions are considered as   special kinds of (Banach) pair frames.  Some frame-like inequalities  for (Banach)  pair frames are presented. The elements that participant  in the construction of (Ba...