2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64276W.B. Johnson has constructed a series of Banach spaces non isomorphic to the Hilbert one that have the hereditarily approximation property (shortly hereditarily AP): all their subspaces also have the AP. All these examples were ''sufficiently'' non-symmetric and this fact allows Johnson to ask: whether there exists any Banach space $X$ with symmetric (or, at least, subsymmetric) basis, distinct from the Hilbert space such that each its subspace has the AP? In this paper is shown that there is a Banach space with a subsymmetric basis (non-equivalent to any symmetric one), which enjoys the hereditarily AP.Latex2e, revised versionFunctional Analysis46B28 (Primary) 46B07, 46B08, 46B20, 46B45 (Secondary)text