Related papers: The Calderon projection over C* algebras

The Dirac-Dolbeault operator for a compact K\"ahler manifold is a special case of a Dirac operator. The Green function for the Dirac Laplacian over a Riemannian manifold with boundary allows to express the values of the sections of the…

We study contractive projections, isometries, and real positive maps on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and…

We develop some tools for manipulating and constructing projections in C*-algebras. These are then applied to give short proofs of some standard projection homotopy results, as well as strengthen some fundamental classical results for…

We pursue the idea of constructing higher spin fields as solutions to twisted Dirac operators. As general results we find that twisted prenormally hyperbolic first order operators (such as the Dirac operator) on globally hyperbolic…

We continue our study of the general theory of possibly nonselfadjoint algebras of operators on a Hilbert space, and modules over such algebras, developing a little more technology to connect `nonselfadjoint operator algebra' with the…

We define two types of pseudo-differential perturbations of the Dirac operator within the framework of the noncommutative geometry. And we obtain the noncommutative residue of the inverse square of these perturbations on 4-dimensional…

Woronowicz introduced the functional calculus for normal operators in Hilbert C*-modules. The aim of this paper is to translate, if possible, some basic properties of the functional calculus in Hilbert spaces to the Hilbert C*-module…

Let A be a C*-algebra, h a Hilbert space and C the CAR algebra over h. We construct a twisted tensor product of A by C such that the two factors are not necessarily one in the relative commutant of the other. The resulting C*-algebra may be…

In a recent paper by M. Mantoiu and M. Ruzhansky, a global pseudo-differential calculus has been developed for unimodular groups of type I. In the present article we generalize the main results to arbitrary locally compact groups of type I.…

We obtain a generalization, for a general compact almost complex manifold, of the well-known K\"{a}hler (or Hodge) identities for K\"{a}hler manifolds involving the commutators of the exterior differential and the Lefschetz operator and its…

Every bounded linear operator on a Hilbert space which is invertible modulo compact operators has a closed range and is, thus, generalized invertible. We consider the analogue question in general $C^*$-algebras and describe the closed…

We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert…

The universal C*-algebra generated by n projections has been described. As an immediate corollary one obtains structure theorem for a pair of projections and the solution to an associated index problem. This puts the study of a pair of…

We single out the concept of concrete Hilbert module over a locally $C^*$-algebra by means of locally bounded operators on certain strictly inductive limits of Hilbert spaces. Using this concept, we construct an operator model for all…

In the context of studying $C^*$-algebras generated by Toeplitz operators acting on the poly-Bergman space $\mathcal{A}^2_{n}(\Pi)$ of the upper half-plane $\Pi$, we introduce a system of all-but-one orthogonal projections in generic…

For a Dirac operator $D_{\bar{g}}$ over a spin compact Riemannian manifold with boundary $(\bar{X},\bar{g})$, we give a natural construction of the Calder\'on projector and of the associated Bergman projector on the space of harmonic…

A Hilbert $C^*$-quad module of finite type has a multi structure of Hilbert $C^*$-bimodules with two finite bases. We will construct a $C^*$-algebra from a Hilbert $C^*$-quad module of finite type and prove its universality subject to…

In this paper, we obtain several extensions of semi-Fredholm theory on Hilbert modules by generalizing in this setting their classical counterparts regarding Weyl operators and Drazin invertible operators.

We study closedness of the range, adjointability and generalized invertibility of modular operators between Hilbert modules over locally C*-algebras of coefficients. Our investigations and the recent results of M. Frank [Characterizing…

We derive a general obstruction to the existence of Riemannian metrics of positive scalar curvature on closed spin manifolds in terms of hypersurfaces of codimension two. The proof is based on coarse index theory for Dirac operators that…