Eigenvalue distribution of integral operators defined by Orlicz kernels.
Entropy numbers of general diagonal operators.
We determine the asymptotic behavior of the entropy numbers of diagonal operators D: lp → lq, (xk) → (skxk), 0 < p,q ≤ ∞, under mild regularity and decay conditions on the generating sequence (σk). Our results extend the known estimates for polynomial and logarithmic diagonals (σk). Moreover, we also consider some exotic intermediate examples like (σk)=exp(-√log k).
Errata to the paper "Banach-Saks property in some Banach sequence spaces" (Ann. Polon. Math. 65 (1997), 193-202)
Erratum to "Algebraic and topological properties of some sets in ℓ₁" (Colloq. Math. 129 (2012), 75-85)
Erratum to “Can ever be amenable?” (Studia Math. 188 (2008), 151-174)
Erratum to the paper "Smooth points of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm" (Colloq. Math. 65 (1993), 157-164)
Examples of k-iterated spreading models
It is shown that for every k ∈ ℕ and every spreading sequence eₙₙ that generates a uniformly convex Banach space E, there exists a uniformly convex Banach space admitting eₙₙ as a k+1-iterated spreading model, but not as a k-iterated one.
Extension of operators from weak*-closed sub-spaces of into C(K) spaces
It is proved that every operator from a weak*-closed subspace of into a space C(K) of continuous functions on a compact Hausdorff space K can be extended to an operator from to C(K).
Extreme points and descriptive sets
A class of closed, bounded, convex sets in the Banach space is shown to be a complete PCA set.