in this paper, we state some results on product of operators with closed rangesand we solve the operator equation txs*- sx*t*= a in the general setting of theadjointable operators between hilbert c*-modules, when ts = 1. furthermore, by usingsome block operator matrix techniques, we nd explicit solution of the operator equationtxs*- sx*t*= a.

We provide a new characterization of the notion of sheaf on an étale groupoid G, in terms of a particular kind of Hilbert module on the quantale O(G) of the groupoid. All the theory is developed in the context of the more general class of quantales known as stable quantal frames, of which examples are easy to construct because their category is algebraic. The homomorphisms of our Hilbert module...

Let M be a Hilbert module of holomorphic functions over a natural function algebra A (Ω), where Ω ⊆Cm is a bounded domain. Let M0 ⊆M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modules Q = M ⊖M0. The invariants are given explicitly in the particula...

Investigating the direct integral decomposition of von Neumann algebras of bounded module operators on self-dual Hilbert W*-modules an equivalence principle is obtained which connects the theory of direct disintegration of von Neumann algebras on separable Hilbert spaces and the theory of von Neumann representations on self-dual Hilbert A-modules with countably generated Apre-dual Hilbert A-mod...

It’s well known that the functional Hilbert space H2 over the unit ball Bd ⊂ C , with kernel function K(z, ω) = 1 1−z1ω1−···−zdωd , admits a natural A(Bd)-module structure. We show the rank of a nonzero submodule M ⊂ H2 is infinity if and only if M is of infinite codimension. Together with Arveson’s dilation theory, our result shows that Hilbert modules stand in stark contrast with Hilbert basi...

X iv :0 90 5. 40 67 v1 [ m at h. FA ] 2 5 M ay 2 00 9 BESSEL TYPE INEQUALITIES IN HILBERT C-MODULES S. S. DRAGOMIR, M. KHOSRAVI AND M. S. MOSLEHIAN Abstract. Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombiari and Boas–Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C∗-mo...

B. Magajna and J. Schweizer showed in 1997 and 1999, respectively, that C*-algebras of compact operators can be characterized by the property that every norm-closed (and coinciding with its biorthogonal complement, resp.) submodule of every Hilbert C*-module over them is automatically an orthogonal summand. We find out further generic properties of the category of Hilbert C*-modules over C*-alg...