scholarly journals On the C*-Algebra of a Locally Injective Surjection and its KMS States

2010 ◽  
Vol 302 (2) ◽  
pp. 403-423 ◽  
Author(s):  
Klaus Thomsen
Keyword(s):  
Kms States ◽  
C Algebra

scholarly journals Boundary quotients of the right Toeplitz algebra of the affine semigroup over the natural numbers

10.53733/90 ◽  
2021 ◽  
Vol 52 ◽  
pp. 109-143
Author(s):  
Astrid An Huef ◽  
Marcelo Laca ◽  
Iain Raeburn
Keyword(s):  
Regular Representation ◽  
Crossed Product ◽  
Ideal Structure ◽  
Toeplitz Algebra ◽  
Natural Numbers ◽  
Kms States ◽  
C Algebra ◽  
Affine Semigroup ◽  
Natural Dynamics ◽  
The Right

We study the Toeplitz $C^*$-algebra generated by the right-regular representation of the semigroup ${\mathbb N \rtimes \mathbb N^\times}$, which we call the right Toeplitz algebra. We analyse its structure by studying three distinguished quotients. We show that the multiplicative boundary quotient is isomorphic to a crossed product of the Toeplitz algebra of the additive rationals by an action of the multiplicative rationals, and study its ideal structure. The Crisp--Laca boundary quotient is isomorphic to the $C^*$-algebra of the group ${\mathbb Q_+^\times}\!\! \ltimes \mathbb Q$. There is a natural dynamics on the right Toeplitz algebra and all its KMS states factor through the additive boundary quotient. We describe the KMS simplex for inverse temperatures greater than one.

scholarly journals KMS states on the C⁎-algebra of a higher-rank graph and periodicity in the path space

2015 ◽  
Vol 268 (7) ◽  
pp. 1840-1875 ◽  
Author(s):  
Astrid an Huef ◽  
Marcelo Laca ◽  
Iain Raeburn ◽  
Aidan Sims
Keyword(s):  
Path Space ◽  
Kms States ◽  
C Algebra ◽  
Higher Rank

scholarly journals KMS states on C*-algebras associated to local homeomorphisms

2014 ◽  
Vol 25 (08) ◽  
pp. 1450066 ◽  
Author(s):  
Zahra Afsar ◽  
Astrid an Huef ◽  
Iain Raeburn
Keyword(s):  
Finite Graph ◽  
Critical Value ◽  
Toeplitz Algebra ◽  
Graph Algebras ◽  
Kms States ◽  
C Algebra ◽  
C Algebras ◽  
Backward Shift ◽  
The One ◽  
Natural Dynamics

For every Hilbert bimodule over a C*-algebra, there are natural gauge actions of the circle on the associated Toeplitz algebra and Cuntz–Pimsner algebra, and hence natural dynamics obtained by lifting these gauge actions to actions of the real line. We study the KMS states of these dynamics for a family of bimodules associated to local homeomorphisms on compact spaces. For inverse temperatures larger than a certain critical value, we find a large simplex of KMS states on the Toeplitz algebra, and we show that all KMS states on the Cuntz–Pimsner algebra have inverse temperature at most this critical value. We illustrate our results by considering the backward shift on the one-sided path space of a finite graph, where we can use recent results about KMS states on graph algebras to see what happens below the critical value. Our results about KMS states on the Cuntz–Pimsner algebra of the shift show that recent constraints on the range of inverse temperatures obtained by Thomsen are sharp.

A new method for approximation of closed convex subsets of B(H)

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6005-6013
Author(s):  
Mahdi Iranmanesh ◽  
Fatemeh Soleimany
Keyword(s):  
Best Approximation ◽  
Numerical Range ◽  
New Method ◽  
C Algebra ◽  
Convex Subsets

In this paper we use the concept of numerical range to characterize best approximation points in closed convex subsets of B(H): Finally by using this method we give also a useful characterization of best approximation in closed convex subsets of a C*-algebra A.

scholarly journals The Poincaré half-space of a C$^*$-algebra

2019 ◽  
Vol 35 (7) ◽  
pp. 2187-2219
Author(s):  
Esteban Andruchow ◽  
Gustavo Corach ◽  
Lázaro Recht
Keyword(s):  
Half Space ◽  
C Algebra

scholarly journals Measuring Multijet Structure of Hadronic Energy Flow or, What is a jet?

1997 ◽  
Vol 12 (30) ◽  
pp. 5411-5529 ◽  
Author(s):  
Fyodor V. Tkachov
Keyword(s):  
Energy Flow ◽  
Mass Spectra ◽  
Analytical Control ◽  
Final States ◽  
C Algebra ◽  
Approximation Errors ◽  
Basic Class ◽  
Jet Algorithms ◽  
Hadronic Energy ◽  
Optimal Recombination

Ambiguities of jet algorithms are reinterpreted as instability wrt small variations of input. Optimal stability occurs for observables possessing property of calorimetric continuity (C-continuity) predetermined by kinematical structure of calorimetric detectors. The so-called C-correlators form a basic class of such observables and fit naturally into QFT framework, allowing systematic theoretical studies. A few rules generate other C-continuous observables. The resulting C-algebra correctly quantifies any feature of multijet structure such as the "number of jets" and mass spectra of "multijet substates." The new observables are physically equivalent to traditional ones but can be computed from final states bypassing jet algorithms which reemerge as a tool of approximate computation of C-observables from data with all ambiguities under analytical control and an optimal recombination criterion minimizing approximation errors.

scholarly journals Nuclear subalgebras of UHF C*-algebras

1986 ◽  
Vol 29 (1) ◽  
pp. 97-100 ◽  
Author(s):  
R. J. Archbold ◽  
Alexander Kumjian
Keyword(s):  
Tensor Product ◽  
Inductive Limit ◽  
Inductive Limits ◽  
C Algebra ◽  
C Algebras ◽  
Finite Dimensional ◽  
The Family ◽  
Algebraic Tensor Product

A C*-algebra A is said to be approximately finite dimensional (AF) if it is the inductive limit of a sequence of finite dimensional C*-algebras(see [2], [5]). It is said to be nuclear if, for each C*-algebra B, there is a unique C*-norm on the *-algebraic tensor product A ⊗B [11]. Since finite dimensional C*-algebras are nuclear, and inductive limits of nuclear C*-algebras are nuclear [16];,every AF C*-algebra is nuclear. The family of nuclear C*-algebras is a large and well-behaved class (see [12]). The AF C*-algebras for a particularly tractable sub-class which has been completely classified in terms of the invariant K0 [7], [5].

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