The stable rank of full corners in C*-algebras

We give a treatment of Rieffel's theory of stable rank for C*-algebras in terms of left invertibility of generalized nonsquare matrices, and prove that if is a full projection in a unital C*-algebra , then the stable rank of the corner is at least as large as the stable rank of .

     

Irreducible * representations of realC*-algebras

In this paper, we show that a topologically irreducible * representation of a realC*-algebra is also algebraically irreducible. Moreover, the properties of pure real states on a realC*-algebra and their left kernels are discussed.Partially supported by the National Natural Science Foundation of China.     

On the spectrum of linear combinations of two projections in C*-algebras

In this note, we study the spectrum and give estimations for the spectral radius of linear combinations of two projections in C*-algebras. We also study the commutator of two projections.     

On the stable rank of simple C*-algebras

It is shown that there exists a simple, finite C*-algebra whose topological (or Bass) stable rank is any given natural number or .

     

Factorization of EP elements in C*-algebras

We offer some extensions to C*-algebra elements of factorization properties of EP operators on a Hilbert space.     

单的迹稳定秩一C*-代数的消去性质

本文证明了一个单的有单位元的迹稳定秩一的C*-代数具有消去律,利用此结果证明了单的有单位元的迹稳定秩一的C*-代数是稳定秩一的.最后讨论了迹稳定秩一的C*-代数的K0群的性质.     

Crossed products of C*-algebras by endomorphisms

The concept of a twisted crossed product associated to a non-classical C^*-dynamical system is introduced and studied. The relationship between a covariant projective representation of the system and the corresponding induced representation of the twisted crossed product is investigated, particularly from the point of view of determining when the induced representation is faithful. Conditions are given on the C^*-dynamical system that ensure nuclearity, simplicity or primeness of the twisted crossed product.     

Von Neumann Regularity and Quadratic Conorms in JB^＊-triples and C^＊-algebras

We revise the notion of von Neumann regularity in JB^＊-triples by finding a new characterisation in terms of the range of the quadratic operator Q（a）. We introduce the quadratic conorm of an element a in a JB^＊-triple as the minimum reduced modulus of the mapping Q（a）. It is shown that the quadratic conorm of a coincides with the infimum of the squares of the points in the triple spectrum of a. It is established that a contractive bijection between JBW^＊-triples is a triple isomorphism if, and only if, it preserves quadratic conorms. The continuity of the quadratic conorm and the generalized inverse are discussed. Some applications to C^＊-algebras and von Neumann algebras are also studied.     

*-representations on Banach *-algebras

We study notions of -bounded linear functionals and represent-
able functionals on Banach *-algebras. An equivalence between these two is established for general Banach *-algebras. In particular, we characterize -bounded linear functionals on Banach *-algebras with approximate identity and isometric involution. In addition, we prove a result on representation of -bounded positive linear functionals in terms of cyclic vectors for the corresponding *-representation.

     

Unitary equivalence of automorphisms of separable C*-algebras

We prove that the automorphisms of any separable C*-algebra that does not have continuous trace are not classifiable by countable structures up to unitary equivalence. This implies a dichotomy for the Borel complexity of the relation of unitary equivalence of automorphisms of a separable unital C*-algebra: Such relation is either smooth or not even classifiable by countable structures.     

KMS states on C*-algebras associated to expansive maps

Using Walters' version of the Ruelle-Perron-Frobenius Theorem we show the existence and uniqueness of KMS states for a certain one-parameter group of automorphisms on a C*-algebra associated to a positively expansive map on a compact metric space.

     

Positive and real-positive solutions to the equation axa*=c in C*-algebras

We obtain new representations for the general positive and real-positive solutions of the equation axa*=c in a C*-algebra using the characterization of positivity based on a matrix representation of an element and the generalized Schur complement. Applications to the equation AXA*=C for operators between Hilbert spaces and for finite matrices are given.     

Linear maps between C*-algebras that are *-homomorphisms at a fixed point

Let A and B be C*-algebras. A linear map T : A → B is said to be a *-homomorphism at an element z ∈ A if ab* = z in A implies T (ab*) = T (a)T (b)* = T (z), and c*d = z in A gives T (c*d) = T (c)*T (d) = T (z). Assuming that A is unital, we prove that every linear map T : A → B which is a *-homomorphism at the unit of A is a Jordan *-homomorphism. If A is simple and infinite, then we establish that a linear map T : A → B is a *-homomorphism if and only if T is a *-homomorphism at the unit of A. For a general unital C*-algebra A and a linear map T : A → B, we prove that T is a *-homomorphism if, and only if, T is a *-homomorphism at 0 and at 1. Actually if p is a non-zero projection in A, and T is a ^?-homomorphism at p and at 1 ? p, then we prove that T is a Jordan *-homomorphism. We also study bounded linear maps that are *-homomorphisms at a unitary element in A.     

KMS states of quasi-free dynamics on Pimsner algebras

A continuous one-parameter group of unitary isometries of a right-Hilbert -bimodule induces a quasi-free dynamics on the Cuntz-Pimsner -algebra of the bimodule and on its Toeplitz extension. The restriction of such a dynamics to the algebra of coefficients of the bimodule is trivial, and the corresponding KMS states of the Toeplitz-Cuntz-Pimsner and Cuntz-Pimsner -algebras are characterized in terms of traces on the algebra of coefficients. This generalizes and sheds light onto various earlier results about KMS states of the gauge actions on Cuntz algebras, Cuntz-Krieger algebras, and crossed products by endomorphisms. We also obtain a more general characterization, in terms of KMS weights, for the case in which the inducing isometries are not unitary, and accordingly, the restriction of the quasi-free dynamics to the algebra of coefficients is nontrivial.     

KMS States for generalized Gauge actions on Cuntz-Krieger algebras

Given a zero-one matrix A we consider certain one-parameter groups of automorphisms of the Cuntz-Krieger algebra , generalizing the usual gauge group, and depending on a positive continuous function H defined on the Markov space _A. The main result consists of an application of Ruelles Perron-Frobenius Theorem to show that these automorphism groups admit a single KMS state.*Partially supported by CNPq.     

Hopf C*-algebras related to the Latin square

A sufficient condition is given for the multiparametric Hopf algebras to be Hopf* -algebras. Then a special subclass of the -algebra related to a Latin square is given. After being completed, its generators are all of norm one.