Banach spaces with a shrinking hyperorthogonal basis

The group of isometries of a Banach space and duality

“…Namely, when X is reflexive (obvious) and, more generally, when X is M -embedded [16, Proposition III.2.2] and, even more generally, when there exists a unique norm-one projection π : X * * * −→ X * with w * -closed kernel [15,Proposition VII.1]. Other condition to get that all the surjective isometries of X * are w * -continuous is to assure that X has a shrinking 1-unconditional basis [26]. On the other hand, the above map is not always surjective, i.e.…”