Let M be a compact spin manifold with a smooth action of the ntorus. Connes and Landi constructed θ-deformations Mθ of M , parameterized by n × n skew-symmetric matrices θ. The Mθ’s together with the canonical Dirac operator (D,H) on M are an isospectral deformation of M . The Dirac operator D defines a Lipschitz seminorm on C(Mθ), which defines a metric on the state space of C(Mθ). We show tha...

Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a) If the Banach space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the norm topology. (b) If the Banach space admits an equivalent rotund norm, then its weak topology is fragmented by a metric. (c) If the Banach space is weakly ...