The purpose of this paper is to initiate a new attack on Arveson’s resistant conjecture, that all graded submodules of the d-shift Hilbert module H are essentially normal. We introduce the stable division property for modules (and ideals): a normed module M over the ring of polynomials in d variables has the stable division property if it has a generating set {f1, . . . , fk} such that every h ...

Motivated by two norm equations used to characterize the Friedrichs angle, this paper studies C*-isomorphisms associated with projections introducing matched triple and semi-harmonious pair of projections. A (P, Q, H) is said be if H a Hilbert C*-module, P Q are on such that their infimum ∧ exists as an element $${\cal L}(H)$$ , where denotes set all adjointable operators H. The C*-subalgebras ...

In this paper, we study the linear dynamical properties of shift operators on some classes Segal algebras. Moreover, characterize hypercyclic generalized bilateral standard Hilbert module.

We show by (counter)example that the intersection of complemented submodules in a Hilbert $C^*$-module is not necessarily complemented, answering an open question from [MR].