We describe the real, complete modules of the Clifford Algebra C(Z), where Z is a real Hilbert space acting by skew-adjoint operators.

We describe the real, complete modules of the Clifford Algebra C(Z), where Z is a real Hilbert space acting by skew-adjoint operators.

For any open, connected and bounded set Ω ⊆ C m , let A be a natural function algebra consisting of functions holomorphic on Ω. Let M be a Hilbert module over the algebra A and M0 ⊆ M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω. Recently the authors have obtained an explicit complete set of unitary invariants for the quotient module Q = M ⊖ M0 in the case of k = 2...

Given an arbitrary countable directed graph G we prove the C∗-envelope of the tensor algebra T+(G) coincides with the universal Cuntz-Krieger algebra associated with G. Our approach is concrete in nature and does not rely on Hilbert module machinery. We show how our results extend to the case of higher rank graphs, where an analogous result is obtained for the tensor algebra of a row-finite k-g...

In this paper we introduce the notion of linking algebra of a Hilbert module over a locally C -algebra and we extend in the context of locally C -algebras a result of Brown, Green and Rie¤el [Paci…c J.,1977] which states that two C -algebras are strongly Morita equivalent if and only if they are isomorphic with two complementary full corners of a C -algebra. Full text