On Some Classes of Primary Banach Spaces

Abstract

A Banach spaceXis calledprimary(respectively,prime)if for every (bounded linear) projectionPonXeitherPXor (I—P)X(respectively,PXwith dimPX =∞ ) is isomorphic toX.It is well-known that C0andlp, 1 ≦p≦ ∞ [8;14] are prime. However, it is unknown whether there are other prime Banach spaces. For a discussion on prime and primary Banach spaces, we refer the reader to [9].