On some subspaces of Banach spaces whose duals are ₁ spaces

@inproceedings{Zippin1969OnSS,
  title={On some subspaces of Banach spaces whose duals are ₁ spaces},
  author={M. Zippin},
  year={1969}
}
We recall that a sequence {xi}i1 in a Banach space X is called a monotone basis of X (see [1, p. 67]) if each xCX has a unique representation x = a IOiixi where {ail} are scalars and the projections Pn on X defined by P.(Ez 1 aixi) = J= 1 aoixi are of norm 1. The purpose of this note is to show that the space c0 (= the space of real sequencesp = {Pn Ix 1 which converge to 0 with IpI = sup,,n P. I) is the minimal infinite dimensional Banach space whose dual is an L1 space, namely