Razvan Anisca

The ergodicity of weak Hilbert spaces

This paper complements a recent result of Dilworth, Ferenczi, Kutzarova and Odell regarding the ergodicity of strongly asymptotic l p spaces. We state this result in a more general form, involving domination relations, and we show that every asymptotically Hilbertian space which is not isomorphic to l 2 is ergodic. In particular, every weak Hilbert space which is not isomorphic to l 2 must be ergodic. Throughout the paper we construct explicitly the maps which establish the fact that the relation E 0 is Borel reducible to isomorphism between subspaces of the Banach spaces involved.

A Technique of Studying Sums of Central Cantor Sets

Thispaperisconcernedwiththestructureofthearithmeticsumofafinitenumberofcentral Cantor sets. The technique used to study this consists of a duality between central Cantor sets and sets of subsums of certain infinite series. One consequence is that the sum of a finite number of central Cantor sets is one of the following: a finite union of closed intervals, homeomorphic to the Cantor ternary set or an M-Cantorval.

On the structure of arithmetic sums of Cantor sets with constant ratios of dissection

We investigate conditions which imply that the topological structure of the arithmetic sum of two Cantor sets with constant ratios of dissection at each step is either: a Cantor set, a finite union of closed intervals, or three mixed models (L, R and M-Cantorval). We obtain general results that apply in particular for the case of homogeneous Cantor sets, thus generalizing the results of Mendes and Oliveira. The method used here is new in this context. We also produce results regarding the arithmetic sum of two affine Cantor sets of a special kind.