相关论文: Order units in a C*-algebra

We study some properies of $Z^{*}$ algebras, thos C^* algebra which all positive elements are zero divisors. We show by means of an example that an extension of a Z* algebra by a Z* algebra is not necessarily Z* algebra. However we prove…

Motivated by Exel's inverse semigroup approach to combinatorial C*-algebras, in a previous work the authors defined an inverse semigroup associated with a labelled space. We construct a representation of the C*-algebra of a labelled space,…

We give some new characterizations of unitaries, isometries, unital operator spaces, unital function spaces, operator systems, C*-algebras, and related objects. These characterizations only employ the vector space and operator space…

Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of characteristic $p$ and $*$ the classical involution of $FG$. The $*$-unitary subgroup of $FG$, denoted by $V_*(FG)$, is defined to be the set of all…

We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*-algebras as…

In this paper, we will define the reduced cross-sectional $C^*$-algebras of $C^*$-algebraic bundles over locally compact groups and show that if a $C^*$-algebraic bundle has the approximation property (defined similarly as in the discrete…

In recent work of the second author, a technical result was proved establishing a bijective correspondence between certain open projections in a C*-algebra containing an operator algebra A, and certain one-sided ideals of A. Here we give…

The purpose of this paper is two-fold: firstly, we give a characterization on the level of non-unital operator systems for when the zero map is a boundary representation. As a consequence, we show that a non-unital operator system arising…

We introduce a new class of operator algebras -- tracially complete C*-algebras -- as a vehicle for transferring ideas and results between C*-algebras and their tracial von Neumann algebra completions. We obtain structure and classification…

We study the uniform property $\Gamma$ for separable simple $C^*$-algebras which have quasitraces and may not be exact. We show that a stably finite separable simple $C^*$-algebra $A$ with strict comparison and uniform property $\Gamma$ has…

For a unital $C^*$-algebra $\mathcal A$ and a subspace $\mathcal B$ of $\mathcal A$, a characterization for a best approximation to an element of $\mathcal A$ in $\mathcal B$ is obtained. As an application, a formula for the distance of an…

We show that unital simple C*-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C^-algebras can be classified by their ordered $K$-theory. We apply this classification result to show that certain…

We show that the tensor product of two unital C*-algebras, one of which is nuclear and admits a unital *-homomorphism from (the building blocks of) the Jiang-Su algebra, has Kadison's similarity property. As a consequence, we obtain that a…

In this paper, we consider $\text{C}^*$-algebras with the ideal property (the ideal property unifies the simple and real rank zero cases). We define two categories related the invariants of the $\text{C}^*$-algebras with the ideal property.…

We investigate the deformation of involution and multiplication in a unital $C^*$-algebra when its norm is fixed. Our main result is to present all multiplications and involutions on a given $C^*$-algebra $\mathcal{A}$ under which…

We introduce the notion of eigenstate of an operator in an abstract C*-algebra, and prove several properties. Most significantly, if the operator is self-adjoint, then every element of its spectrum has a corresponding eigenstate.

Let $n$ be a positive integer. We introduce a concept, which we call the $n$-filling property, for an action of a group on a separable unital $C^*$-algebra $A$. If $A=C(\Omega)$ is a commutative unital $C^*$-algebra and the action is…

We show that semiprojectivity of a C*-algebra is preserved when passing to C*-subalgebras of finite codimension. In particular, any pullback of two semiprojective C*-algebras over a finite-dimensional C*-algebra is again semiprojective.

We present an introductory survey to first order logic for metric structures and its applications to C*-algebras.

We obtain a kind of structure theorem for the automorphism group ${\rm Aut}{\cal A}$ of a unital C$^{*}$-algebra ${\cal A}$. According to it, ${\rm Aut}{\cal A}$ can be regarded as a subgroup of the semi-direct product of direct product…