Related papers: Null projections and noncommutative function theor…
We generalize some facts about function algebras to operator algebras, using the `noncommutative Shilov boundary' or $C^*$-envelope first considered by Arveson. In the first part we study and characterize complete isometries between…
We associate to each unital $C^*$-algebra $A$ a geometric object---a diagram of topological spaces representing quotient spaces of the noncommutative space underlying $A$---meant to serve the role of a generalized Gel'fand spectrum. After…
We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, we prove a…
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…
For differential operators which are invariant under the action of an abelian group Bloch theory is the preferred tool to analyze spectral properties. By shedding some new non-commutative light on this we motivate the introduction of a…
In this paper we study nonlinear interpolation problems for interpolation and peak-interpolation sets of function algebras. The subject goes back to the classical Rudin-Carleson interpolation theorem. In particular, we prove the following…
The concept of regularity in the meta-topological setting of projections in the double dual of a C*-algebra addresses the interrelations of a projection p with its closure, for instance in the form that such projections act identically, in…
We begin a program of generalizing basic elements of the theory of comparison, equivalence, and subequivalence, of elements in C*-algebras, to the setting of more general algebras. In particular, we follow the recent lead of Lin, Ortega,…
We initiate a study of projections and modules over a noncommutative cylinder, a simple example of a noncompact noncommutative manifold. Since its algebraic structure turns out to have many similarities with the noncommutative torus, one…
Every partial algebra is the colimit of its total subalgebras. We prove this result for partial Boolean algebras (including orthomodular lattices) and the new notion of partial C*-algebras (including noncommutative C*-algebras), and…
By appropriate choices of elements in the underlying iterated function system, methodology of fractal interpolation entitles one to associate a family of continuous self-referential functions with a prescribed real-valued continuous…
We study operator spaces, operator algebras, and operator modules, from the point of view of the `noncommutative Shilov boundary'. In this attempt to utilize some `noncommutative Choquet theory', we find that Hilbert C$^*-$modules and their…
The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr's idea that the empirical content of quantum physics is accessible…
We construct some separable infinite dimensional homogeneous Hilbertian operator spaces which generalize the row and column spaces R and C. We show that separable infinite-dimensional Hilbertian JC*-triples are completely isometric to an…
Examples of Fell algebras with compact spectrum and trivial Dixmier-Douady invariant are constructed to illustrate differences with the case of continuous trace $C^*$-algebras. At the level of the spectrum, this translates to only assuming…
We describe and characterize the contractively decomposable projections on noncommutative $\mathrm{L}^p$-spaces. Our result relies on a new lifting result for decomposable maps of independent interest and on some tools from ergodic theory.…
We study the theory of a Hilbert space H as a module for a unital C*-algebra A from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are…
We extend the Gelfand-Naimark duality of commutative C*-algebras, "A COMMUTATIVE C*-ALGEBRA -- A LOCALLY COMPACT HAUSDORFF SPACE" to "A C*-ALGEBRA--A QUOTIENT OF A LOCALLY COMPACT HAUSDORFF SPACE". Thus, a C*-algebra is isomorphic to the…
The class of $\D$-locally nilpotent algebras (introduced in the paper) is a wide generalization of the algebras of differential operators on commutative algebras. Examples includes all the rings $\CD (A)$ of differential operators on…
For a tuple $A=(A_0, A_1, ..., A_n)$ of elements in a unital Banach algebra ${\mathcal B}$, its {\em projective spectrum} $p(A)$ is defined to be the collection of $z=[z_0, z_1, ..., z_n]\in \pn$ such that $A(z)=z_0A_0+z_1A_1+... +z_nA_n$…