Characterization of symmetric points in lpn-spaces

We characterize the left-symmetric points as well as the right-symmetric points in the sense of Birkhoff-James orthogonality, of the Banach spaces lpn (1≤p≤∞). As an application of our study, we produce an elementary proof of the well-known result: T is an isometry on lpn (p≠ 1,2,∞) if and only if T is a signed permutation. This illustrates the pivotal role played by the set of left-symmetric points in determining the isometry group of a given Banach space.