Banach spaces with trivial isometries
A Banach space is said to have trivial isometries if the only (onto) isometries are plus or minus the identity. (Hence we are considering Banach spaces over the reals.) We show each separable Banach space has an equivalent norm with only trivial isometries. Also an equivalent norm on a non-separable Hilbert space with only trivial isometries is constructed. The constructions are based on ''pimples'', a way of decreasing the norm so that the unit ball has two ''cones'' added.
scientific article; zbMATH DE number 4004903