An example of a reflexive Banach space with an uncomplemented isometric subspace

Abstract

We present an example of a reflexive Banach space $X$ with a basis $(e_i{)}_{i=1}^{\infty }$ 1-equivalent to its subsequence $(e_{2i}{)}_{i=1}^{\infty }$. The closed subspace of $X$ spanned by the latter is not complemented in $X$, whereas the subsequence $(e_{2i-1}{)}_{i=1}^{\infty }$ is unconditional.

arXiv comment14 pages, the construction simplified and additional features of the built space, concerning unconditional structure of its subspaces, exhibited