Each operator in L (lp,lr) (1 ≤ r < p < ∞) is compact.
It is known that each bounded operator from lp → lris compact. The purpose of this paper is to present a very simple proof of this useful fact.
Eigenvalue distribution of integral operators defined by Besov-Orlicz kernels.
Embedding l∞N-cubes in finite-dimensional 1-subsymmetric spaces.
Embeding weakly compact sets
Erratum to “Can ever be amenable?” (Studia Math. 188 (2008), 151-174)
Euclidean arrangements in Banach spaces
We study the way in which the Euclidean subspaces of a Banach space fit together, somewhat in the spirit of the Kashin decomposition. The main tool that we introduce is an estimate regarding the convex hull of a convex body in John's position with a Euclidean ball of a given radius, which leads to a new and simplified proof of the randomized isomorphic Dvoretzky theorem. Our results also include a characterization of spaces with nontrivial cotype in terms of arrangements of Euclidean subspaces.
Extremal sections of complex -balls, 0 < p ≤ 2
We study the extremal volume of central hyperplane sections of complex n-dimensional -balls with 0 < p ≤ 2. We show that the minimum corresponds to hyperplanes orthogonal to vectors ξ = (ξ¹,...,ξⁿ) ∈ ℂⁿ with |ξ¹| = ... = |ξⁿ|, and the maximum corresponds to hyperplanes orthogonal to vectors with only one non-zero coordinate.
Extreme norms on