Two remarks on the Franklin system

Abstract

The aim of this note is to present two observations about the classical Franklin system. First we show that the Franklin system, when considered in the space generated by special atoms (as defined and studied by Soares de Souza in [11] and ]12]) is an unconditional basis equivalent to the unit vector basis in l1. In our second result we give conceptually simpler proofs and some extensions of the results of Bočkariov's [1] about the conjugate Franklin system.