# 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} }

- Published 1969
DOI:10.1090/S0002-9939-1969-0246094-0

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

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