scholarly journals On reduced amalgamated free products of C*-algebras and the MF property

2012 ◽  
Vol 61 (5) ◽  
pp. 1911-1923 ◽  
Author(s):  
Jonas Seebach
2016 ◽  
Vol 50 (1) ◽  
pp. 39-47
Author(s):  
Qihui Li ◽  
Don Hadwin ◽  
Jiankui Li ◽  
Xiujuan Ma ◽  
Junhao Shen

2018 ◽  
Vol 149 (04) ◽  
pp. 869-876 ◽  
Author(s):  
Kenneth R. Davidson ◽  
Evgenios T. A. Kakariadis

AbstractWe give a general method of extending unital completely positive maps to amalgamated free products of C*-algebras. As an application, we give a dilation theoretic proof of Boca's Theorem.


2001 ◽  
Vol 44 (2) ◽  
pp. 425-444 ◽  
Author(s):  
Kenneth J. Dykema ◽  
Dimitri Shlyakhtenko

AbstractLet $H$ be a full Hilbert bimodule over a $C^*$-algebra $A$. We show that the Cuntz–Pimsner algebra associated to $H$ is exact if and only if $A$ is exact. Using this result, we give alternative proofs for exactness of reduced amalgamated free products of exact $C^*$-algebras. In the case in which $A$ is a finite-dimensional $C^*$-algebra, we also show that the Brown–Voiculescu topological entropy of Bogljubov automorphisms of the Cuntz–Pimsner algebra associated to an $A,A$ Hilbert bimodule is zero.AMS 2000 Mathematics subject classification: Primary 46L08. Secondary 46L09; 46L54


2005 ◽  
Vol 15 (05n06) ◽  
pp. 869-874 ◽  
Author(s):  
MARTIN R. BRIDSON

We consider the growth functions βΓ(n) of amalgamated free products Γ = A *C B, where A ≅ B are finitely generated, C is free abelian and |A/C| = |A/B| = 2. For every d ∈ ℕ there exist examples with βΓ(n) ≃ nd+1βA(n). There also exist examples with βΓ(n) ≃ en. Similar behavior is exhibited among Dehn functions.


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