We use the fixed point alternative theorem to prove that, under suitable conditions, every A-valued approximate isometry on a Hilbert C∗-module over the C∗-algebra A can be approximated by a unique A-valued isometry. AMS subject classifications: Primary 39B52, 39B82, 46B04, 46L08; Secondary 47H10

We show that the unit ball of a full Hilbert C∗-module is sequentially compact in a certain weak topology if and only if the underlying C∗-algebra is finite dimensional. This provides an answer to the question posed in J. Chmieliński et al [Perturbation of the Wigner equation in inner product C∗-modules, J. Math. Phys. 49 (2008), no. 3, 033519].

In this paper, the principal tool to describe transversal polymatroids with Gorenstein base ring is polyhedral geometry, especially the Danilov−Stanley theorem for the characterization of canonical module. Also, we compute the a − invariant and the Hilbert series of base ring associated to this class of transversal polymatroids.