Basic sequences and spaceability in \(\ell_p\) spaces (Q2444475)

The authors solve, in the negative, the following intriguing open problem posed by R.\,M.\thinspace Aron and V.\,\thinspace Gurariy in 2003: Is there an infinite-dimensional closed subspace \(X\) of \(l_{\infty }\) such that every nonzero element of \(X\) has only a finite number of zero coordinates? In fact, the paper contains several other related results, also involving the case of \(l_{p}\) spaces. The proofs are deep and quite technical, and need deep insights on basic sequences in \(l_{p}\) spaces.