It is obtained a Wold-type decomposition for an adjointable isometry on a Hilbert C∗-module which is sequentially complete with respect to some locally convex topology, denoted by s. Particularly self-dual Hilbert C∗-modules satisfy this condition. Finally, as an application we shall give a new proof of the Wold decomposition theorem for discrete stationary processes in complete correlated acti...

We compute the Hilbert coefficients of a graded module with pure resolution and discuss lower and upper bounds for these coefficients for arbitrary graded modules.

Let A be a fixed C*-algebra. In an arbitrary finitely generated projective A-module V ⊆ An, a spherical tight A-frame is a set of of k, k > n, elements f1, . . . , fk such that the associated matrix F = [f1, . . . , fk] up-to a constant multiple is a partial isometry of the Hilbert structure on the projective finitely generated A-module V . The space FA k,n of all such A-frames form a C*-algebr...

Jim Williams died in 1983. The surviving three authors are pleased to dedicate this paper to his memory. Abstract. Let C denote the category of Hilbert modules which are similar to con-tractive Hilbert modules. It is proved that if H 0 ; H 2 C and if H 1 is similar to an isometric Hilbert module, then the sequence 0 ! H 0 ! H ! H 1 ! 0 splits. Thus the isometric Hilbert modules are projective i...

We prove that an arbitrary (not necessarily countably generated) Hilbert G −A module on a G − C∗ algebra A admits an equivariant embedding into a trivial G−A module, provided G is a compact Lie group and its action on A is ergodic.

The module of splines on a polyhedral complex can be viewed as the syzygy module of its dual graph with edges weighted by powers of linear forms. When the assignment of linear forms to edges meets certain conditions, we can decompose the graph into disjoint cycles without changing the isomorphism class of the syzygy module. Thus we can use this decomposition to compute the homological dimension...