scholarly journals HIGHER-RANK GRAPHS AND THEIR $C^*$-ALGEBRAS

2003 ◽  
Vol 46 (1) ◽  
pp. 99-115 ◽  
Author(s):  
Iain Raeburn ◽  
Aidan Sims ◽  
Trent Yeend
Keyword(s):  
Subject Classification ◽  
Uniqueness Theorems ◽  
Local Convexity ◽  
Convexity Condition ◽  
Primary 46L05 ◽  
C Algebras ◽  
Higher Rank

AbstractWe consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz–Krieger algebras. We describe a variant of the Cuntz–Krieger relations which applies to graphs with sources, and describe a local convexity condition which characterizes the higher-rank graphs that admit a non-trivial Cuntz–Krieger family. We then prove versions of the uniqueness theorems and classifications of ideals for the $C^*$-algebras generated by Cuntz–Krieger families.AMS 2000 Mathematics subject classification: Primary 46L05

scholarly journals A NON-EXTENDABLE BOUNDED LINEAR MAP BETWEEN C*-ALGEBRAS

2001 ◽  
Vol 44 (2) ◽  
pp. 241-248 ◽  
Author(s):  
Narutaka Ozawa
Keyword(s):  
Linear Extension ◽  
Subject Classification ◽  
Primary 46L05 ◽  
Bounded Linear ◽  
Linear Map ◽  
C Algebras ◽  
Secondary 46L07

AbstractWe present an example of a $C^*$-subalgebra $A$ of $\mathbb{B}(H)$ and a bounded linear map from $A$ to $\mathbb{B}(K)$ which does not admit any bounded linear extension. This generalizes the result of Robertson and gives the answer to a problem raised by Pisier. Using the same idea, we compute the exactness constants of some Q-spaces. This solves a problem raised by Oikhberg. We also construct a Q-space which is not locally reflexive.AMS 2000 Mathematics subject classification: Primary 46L05. Secondary 46L07

scholarly journals Uniqueness theorems for topological higher-rank graph $C^*$-algebras

2017 ◽  
Vol 146 (2) ◽  
pp. 669-684 ◽  
Author(s):  
Jean Renault ◽  
Aidan Sims ◽  
Dana P. Williams ◽  
Trent Yeend
Keyword(s):  
Uniqueness Theorems ◽  
C Algebras ◽  
Higher Rank

scholarly journals INVOLUTION AND THE HAAGERUP TENSOR PRODUCT

2001 ◽  
Vol 44 (2) ◽  
pp. 317-322 ◽  
Author(s):  
Ajay Kumar
Keyword(s):  
Tensor Product ◽  
Banach Algebra ◽  
Subject Classification ◽  
Primary 46L05 ◽  
C Algebras

AbstractWe show that the involution $\theta(a\otimes b)=a^*\otimes b^*$ on the Haagerup tensor product $A\otimes_{\mrm{H}}B$ of $C^*$-algebras $A$ and $B$ is an isometry if and only if $A$ and $B$ are commutative. The involutive Banach algebra $A\otimes_{\mrm{H}}A$ arising from the involution $a\otimes b\to b^*\otimes a^*$ is also studied.AMS 2000 Mathematics subject classification: Primary 46L05; 46M05

scholarly journals C*-ALGEBRAS THAT ARE ISOMORPHIC AFTER TENSORING AND FULL PROJECTIONS

2004 ◽  
Vol 47 (3) ◽  
pp. 659-668
Author(s):  
Kazunori Kodaka
Keyword(s):  
Matrix Algebra ◽  
Subject Classification ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Primary 46L05 ◽  
C Algebra ◽  
C Algebras ◽  
Necessary And Sufficient

AbstractLet $A$ be a unital $C^*$-algebra and for each $n\in\mathbb{N}$ let $M_n$ be the $n\times n$ matrix algebra over $\mathbb{C}$. In this paper we shall give a necessary and sufficient condition that there is a unital $C^*$-algebra $B$ satisfying $A\not\cong B$ but for which $A\otimes M_n\cong B\otimes M_n$ for some $n\in\mathbb{N}\setminus\{1\}$. Also, we shall give some examples of unital $C^*$-algebras satisfying the above property.AMS 2000 Mathematics subject classification: Primary 46L05

scholarly journals Spatial realisations of KMS states on the C⁎-algebras of higher-rank graphs

2015 ◽  
Vol 427 (2) ◽  
pp. 977-1003 ◽  
Author(s):  
Astrid an Huef ◽  
Sooran Kang ◽  
Iain Raeburn
Keyword(s):  
Kms States ◽  
C Algebras ◽  
Higher Rank

scholarly journals ON THE CLASSIFICATION OF NUCLEAR C*-ALGEBRAS

2002 ◽  
Vol 85 (1) ◽  
pp. 168-210 ◽  
Author(s):  
MARIUS DADARLAT ◽  
SØREN EILERS
Keyword(s):  
Subject Classification ◽  
Unified Approach ◽  
C Algebras ◽  
Starting Point ◽  
K Theory

We employ results from KK-theory, along with quasidiagonality techniques, to obtain wide-ranging classification results for nuclear C*-algebras. Using a new realization of the Cuntz picture of the Kasparov groups we show that two morphisms inducing equal KK-elements are approximately stably unitarily equivalent. Using K-theory with coefficients to associate a partial KK-element to an approximate morphism, our result is generalized to cover such maps. Conversely, we study the problem of lifting a (positive) partial KK-element to an approximate morphism. These results are employed to obtain classification results for certain classes of quasidiagonal C*-algebras introduced by H. Lin, and to reprove the classification of purely infinite simple nuclear C*-algebras of Kirchberg and Phillips. It is our hope that this work can be the starting point of a unified approach to the classification of nuclear C*-algebras.2000 Mathematical Subject Classification: primary 46L35; secondary 19K14, 19K35, 46L80.

scholarly journals Simplicity of C*-algebras associated to higher-rank graphs

2007 ◽  
Vol 39 (2) ◽  
pp. 337-344 ◽  
Author(s):  
David I. Robertson ◽  
Aidan Sims
Keyword(s):  
C Algebras ◽  
Higher Rank

scholarly journals The C∗-algebras of finitely aligned higher-rank graphs

2004 ◽  
Vol 213 (1) ◽  
pp. 206-240 ◽  
Author(s):  
Iain Raeburn ◽  
Aidan Sims ◽  
Trent Yeend
Keyword(s):  
C Algebras ◽  
Higher Rank

Representations of higher-rank graph C⁎-algebras associated to Λ-semibranching function systems

2018 ◽  
Vol 468 (2) ◽  
pp. 766-798 ◽  
Author(s):  
Carla Farsi ◽  
Elizabeth Gillaspy ◽  
Palle Jorgensen ◽  
Sooran Kang ◽  
Judith Packer
Keyword(s):  
C Algebras ◽  
Higher Rank
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