A basis of Rn with good isometric properties and some applications to denseness of norm attaining operators

We characterize real Banach spaces Y such that the pair (ℓ∞n,Y) has the Bishop-Phelps-Bollobás property for operators. To this purpose it is essential using an appropriate basis of the domain space Rn. As a consequence of the mentioned characterization, we provide examples of spaces Y satisfying such property. For instance, finite-dimensional spaces, uniformly convex spaces, uniform algebras and L1(μ) (μ a positive measure) satisfy the previous property.