相关论文: A Reduction theorem for $AH$ algebras with ideal p…

Let $A$ be an $AH$ algebra $A=\lim\limits_{n\to \infty}(A_{n}=\bigoplus\limits_{i=1}\limits^{t_{n}}P_{n,i}M_{[n,i]}(C(X_{n,i}))P_{n,i}, \phi_{n,m})$, where $X_{n,i}$ are compact metric spaces, $t_{n}$ and $[n,i]$ are positive integers, and…

A $C^{*}$-algebra $A$ has ideal property if any ideal $I$ of $A$ is generated as a closed two sided ideal by the projections inside the ideal. Suppose that the limit $C^{*}$-algebra $A$ of inductive limit of direct sums of matrix algebras…

An ATAI (or ATAF, respectively) algebra, introduced in [Jiang1] (or in [Fa] respectively) is an inductive limit $\lim\limits_{n\rightarrow\infty}(A_{n}=\bigoplus\limits_{i=1}A_{n}^{i},\phi_{nm})$, where each $A_{n}^{i}$ is a simple…

Let $A$ be the inductive limit of a sequence $$A_1\, \xrightarrow{\phi_{1,2}} \,A_2\,\xrightarrow{\phi_{2,3}} \,A_3\rightarrow\cdots$$ with $A_n=\oplus_{i=1}^{n_i}A_{[n,i]}$, where all the $A_{[n,i]}$ are Elliott-Thomsen algebras and…

A $C^*$-algebra is said to have the LP property if the linear span of projections is dense in a given algebra. In the first part of this paper, we show that an AH algebra $A = \underrightarrow{\lim}(A_i,\phi_i)$ has the LP property if and…

For a locally compact Hausdorff space $X$ and a $C^*$-algebra $A$ with only finitely many closed ideals, we discuss a characterization of closed ideals of $C_0(X,A) $ in terms of closed ideals of $A$ and certain (compatible) closed…

We show that for a large class of C*-algebras $\mathcal{A}$, containing arbitrary direct limits of separable type I C*-algebras, the following statement holds: If $A\in \mathcal{A}$ and $B$ is a simple projectionless C*-algebra with trivial…

We show that if A is a separable, nuclear, O_infty-absorbing (or strongly purely infinite) C*-algebra, which is homotopic to zero in an ideal-system preserving way, then A is the inductive limit of C*-algebras of the form M_k(C_0(G,v)),…

We say that an inclusion of an algebra $A$ into a $C^*$-algebra $B$ has the ideal separation property if closed ideals in $B$ can be recovered by their intersection with $A$. Such inclusions have attractive properties from the point of view…

Given a conditional expectation $P$ from a C*-algebra $B$ onto a C*-subalgebra $A$, we observe that induction of ideals via $P$, together with a map which we call co-induction, forms a Galois connection between the lattices of ideals of $A$…

Following up on previous work, we prove a number of results for C*-algebras with the weak ideal property or topological dimension zero, and some results for C*-algebras with related properties. Some of the more important results include:…

Let A be a commutative ring and I an ideal of A with a reduction Q. In this paper we give an upper bound on the reduction number of I with respect to Q, when a suitable family of ideals in A is given. As a corollary it follows that if some…

For $C^*$-algebras $A_1, A_2$ the map $(I_1,I_2)\to ker(q_{I_1}\otimes q_{I_2})$ from $Id^{\prime}(A_1)\times Id^{\prime}(A_2)$ into $Id^{\prime}(A_1\otimes_{\mathrm{min}} A_2) is a homeomorphism onto its image which is dense in the range.…

In this thesis we explore the the possibility of characterising C* algebras by their (non-isometric) Banach algebra structure alone. We introduce a property of Banach algebras, the Total Reduction Property, and conjecture that a Banach…

We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursive subhomogeneous algebras, and they have an inductive…

It is shown that a C*-algebra of the form C(X,U), where U is a UHF algebra, is not an inductive limit of subhomogeneous C*-algebras of topological dimension less than that of X. This is in sharp contrast to dimension-reduction phenomenon in…

We show that a separable C*-algebra is an inductive limits of projective C*-algebras if and only if it has trivial shape, that is, if it is shape equivalent to the zero C*-algebra. In particular, every contractible C*-algebra is an…

We consider unital simple inductive limits of generalized dimension drop C*-algebras They are so-called ASH-algebras and include all unital simple AH-algebras and all dimension drop $C^*$-algebras. Suppose that $A$ is one of these…

This paper is about the reduced group C*-algebras of real reductive groups, and about Hilbert C*-modules over these C*-algebras. We shall do three things. First we shall apply theorems from the tempered representation theory of reductive…

We show that every proper, dense ideal in a C*-algebra is contained in a prime ideal. It follows that a subset generates a C*-algebra as a not necessarily closed ideal if and only if it is not contained in any prime ideal. This allows us to…