On thickness and thinness of Banach spaces

Abstract

The aim of this note is to complement and extend some recent results on Whitley's indices of thinness and thickness in three main directions. Firstly, we investigate both the indices when forming ℓp-sums of Banach spaces, and obtain formulas which show that they behave rather differently. Secondly, we consider the relation of the indices of the space and a subspace. Finally, every Banach space X containing a copy of c0 can be equivalently renormed so that in the new norm c0 is an M-ideal in X and both the thickness and thinness index of X equal 1.2010 Mathematics Subject Classification. 46B20; 46B03.