相关论文: C*-algebra generated by projections

Topological quivers are generalizations of directed graphs in which the sets of vertices and edges are locally compact Hausdorff spaces. Associated to such a topological quiver Q is a C*-correspondence, and from this correspondence one may…

We prove a reduction theorem for capacity of positive maps of finite dimensional C*-algebras, thus reducing the computation of capacity to the case when the image of a nonscalar projection is never a projection.

In [BEZ] the notion of a complete one-sided M-ideal for an operator space X was introduced as a generalization of Alfsen and Effros' notion of an M-ideal for a Banach space [AE72]. In particular, various equivalent formulations of complete…

Let $M$ be a K\"ahler manifold with complex structure $J$ and K\"ahler metric $g$. A c-projective vector field is a vector field on $M$ whose flow sends $J$-planar curves to $J$-planar curves, where $J$-planar curves are analogs of what…

This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules, which constitutes the algebraic version of the vector bundles in differential geometry. We adopt the…

Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and…

It is shown how a C*-algebra representation of the transformations of a physical system can be derived from two operational postulates: 1) the existence of dynamically independent systems}; 2) the existence of symmetric faithful states.…

It is shown that a strongly self-absorbing C*-algebra is of real rank zero and absorbs the Jiang-Su algebra if it contains a nontrivial projection. We also consider cases where the UCT is automatic for strongly self-absorbing C*-algebras,…

Let $(P_1,...,P_n)$ be an $n$--tuple of projections in a unital $C^*$--algebra $\aa$. We say $\pn$ is complete in $\aa$ if $\aa$ is the linear direct sum of the closed subspaces $P_1\aa,...,P_n\aa$. In this paper, we give some necessary and…

We develop a general framework to deal with the unitary representations of quantum groups using the language of C*-algebras. Using this framework, we prove that the duality holds in a general context. This extends the framework of the…

One introduces the notion of C*-algebra with polarization which could be considered as the quantum Kahler structure. The connection of these algebras with Kostant-Souriou geometric quantization is shown. The theory of polarized C*-algebra…

For a finitely aligned k-graph $\Lambda$ with X a set of vertices in $\Lambda$ we define a universal C*-algebra called $C^*(\Lambda,X)$ generated by partial isometries. We show that $C^*(\Lambda,X)$ is isomorphic to the corner…

Many interesting examples of operator algebras, both self-adjoint and non-self-adjoint, can be constructed from directed graphs. In this survey, we overview the construction of $C^*$-algebras from directed graphs and from two…

We compute the $K$-theory of comparison $C^*$-algebra associated to a manifold with corners. These comparison algebras are an example of the abstract pseudodifferential algebras introduced by Connes and Moscovici \cite{M3}. Our calculation…

I introduce yet another way to associate a C*-algebra to a graph and construct a simple nuclear C*-algebra that has irreducible representations both on a separable and a nonseparable Hilbert space.

Cuntz algebra $\mathcal O_2$ is the universal $C^*$-algebra generated by two isometries $s_1, s_2$ satisfying $s_1s_1^*+s_2s_2^*=1$. This is separable, simple, infinite $C^*$-algebra containing a copy of any nuclear $C^*$-algebra. The…

We give a detailed survey of the theory of quasidiagonal C*-algebras. The main structural results are presented and various functorial questions around quasidiagonality are discussed. In particular we look at what is currently known (and…

A braided category of C*-algebras is constructed. Its objects are C*-algebras endowed with an action of the group R, its morphisms are C*-algebras morphisms intertwining the action of R, the crossed product of its two objects essentially…

Spielberg's construction of C*-algebras from left cancellative small categories is a common generalization for most C*-algebras one would consider to come from ``combinatorial data,'' including graph and $k$-graph C*-algebras, Li's…

We compute K-theory for ring C*-algebras in the case of higher roots of unity and thereby completely determine the K-theory for ring C*-algebras attached to rings of integers in arbitrary number fields.