On partial isometries in C*-algebras

2011 ◽  
Vol 205 (1) ◽  
pp. 71-82 ◽  
Author(s):  
M. Laura Arias ◽  
Mostafa Mbekhta
Keyword(s):  
Partial Isometries ◽  
C Algebras

scholarly journals CUNTZ–PIMSNER C*-ALGEBRAS ASSOCIATED WITH SUBSHIFTS

2008 ◽  
Vol 19 (01) ◽  
pp. 47-70 ◽  
Author(s):  
TOKE MEIER CARLSEN
Keyword(s):  
Partial Isometries ◽  
C Algebra ◽  
C Algebras ◽  
Shift Space

By using C*-correspondences and Cuntz–Pimsner algebras, we associate to every subshift (also called a shift space) 𝖷 a C*-algebra [Formula: see text], which is a generalization of the Cuntz–Krieger algebras. We show that [Formula: see text] is the universal C*-algebra generated by partial isometries satisfying relations given by 𝖷. We also show that [Formula: see text] is a one-sided conjugacy invariant of 𝖷.

Partial isometries and an invariant of C*-algebras

2011 ◽  
Vol 27 (4) ◽  
pp. 799-806 ◽  
Author(s):  
Hong Liang Yao ◽  
Xiao Chun Fang
Keyword(s):  
Partial Isometries ◽  
C Algebras

scholarly journals Characterizations of tripotents in JB*-triples

2006 ◽  
Vol 99 (1) ◽  
pp. 147 ◽  
Author(s):  
Remo V. Hügli
Keyword(s):  
Unit Ball ◽  
Partial Order ◽  
Facial Structure ◽  
Partial Isometries ◽  
C Algebras ◽  
Metric Characterization

The set $\mathcal{U}(A)$ of tripotents in a $\mathrm{JB}^*$-triple $A$ is characterized in various ways. Some of the characterizations use only the norm-structure of $A$. The partial order on $\mathcal{U}(A)$ as well as $\sigma$-finiteness of tripotents are described intrinsically in terms of the facial structure of the unit ball $A_1$ in $A$, i.e. without reference to the (pre-)dual of $A$. This extends similar results obtained in [6] and simplifies the metric characterization of partial isometries in $C^*$-algebras found in [1](cf. [8].

Weighted partial isometries and weighted-EP elements in C*-algebras

2015 ◽  
Vol 265 ◽  
pp. 17-30
Author(s):  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Partial Isometries ◽  
C Algebras

scholarly journals $C^*$-algebras arising from Dyck systems of topological Markov chains

2011 ◽  
Vol 109 (1) ◽  
pp. 31 ◽  
Author(s):  
Kengo Matsumoto
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Chain Rule ◽  
Irreducible Matrix ◽  
Partial Isometries ◽  
C Algebra ◽  
C Algebras ◽  
Graph System ◽  
Infinite Sequences

Let $A$ be an $N \times N$ irreducible matrix with entries in $\{0,1\}$. We define the topological Markov Dyck shift $D_A$ to be a nonsofic subshift consisting of bi-infinite sequences of the $2N$ brackets $(_1,\dots,(_N,)_1,\dots,)_N$ with both standard bracket rule and Markov chain rule coming from $A$. It is regarded as a subshift defined by the canonical generators $S_1^*,\dots, S_N^*, S_1,\dots, S_N$ of the Cuntz-Krieger algebra $\mathcal{O}_A$. We construct an irreducible $\lambda$-graph system $\mathcal{L}^{{\mathrm{Ch}}(D_A)}$ that presents the subshift $D_A$ so that we have an associated simple purely infinite $C^*$-algebra $\mathcal{O}_{\mathcal{L}^{{\mathrm{Ch}}(D_A)}}$. We prove that $\mathcal{O}_{\mathcal{L}^{{\mathrm{Ch}}(D_A)}}$ is a universal unique $C^*$-algebra subject to some operator relations among $2N$ generating partial isometries.

scholarly journals CO-UNIVERSAL C*-ALGEBRAS ASSOCIATED TO APERIODIC k-GRAPHS

2013 ◽  
Vol 56 (3) ◽  
pp. 537-550
Author(s):  
SOORAN KANG ◽  
AIDAN SIMS
Keyword(s):  
Hilbert Space ◽  
Toeplitz Algebra ◽  
Partial Isometries ◽  
C Algebras

AbstractWe construct a representation of each finitely aligned aperiodic k-graph Λ on the Hilbert space $\mathcal{H}^{\rm ap}$ with basis indexed by aperiodic boundary paths in Λ. We show that the canonical expectation on $\mathcal{B}(\mathcal{H}^{\rm ap})$ restricts to an expectation of the image of this representation onto the subalgebra spanned by the final projections of the generating partial isometries. We then show that every quotient of the Toeplitz algebra of the k-graph admits an expectation compatible with this one. Using this, we prove that the image of our representation, which is canonically isomorphic to the Cuntz–Krieger algebra, is co-universal for Toeplitz–Cuntz–Krieger families consisting of non-zero partial isometries.

scholarly journals K-Theory for Semigroup C*-Algebras and Partial Crossed Products

2021 ◽  
Author(s):  
Xin Li
Keyword(s):  
Inverse Semigroups ◽  
Crossed Products ◽  
Partial Isometries ◽  
C Algebras ◽  
Regular Representations ◽  
K Theory ◽  
New Applications ◽  
Theory Formula

AbstractUsing the Baum–Connes conjecture with coefficients, we develop a K-theory formula for reduced C*-algebras of strongly 0-E-unitary inverse semigroups, or equivalently, for a class of reduced partial crossed products. This generalizes and gives a new proof of previous K-theory results of Cuntz, Echterhoff and the author. Our K-theory formula applies to a rich class of C*-algebras which are generated by partial isometries. For instance, as new applications which could not be treated using previous results, we discuss semigroup C*-algebras of Artin monoids, Baumslag-Solitar monoids and one-relator monoids, as well as C*-algebras generated by right regular representations of semigroups of number-theoretic origin, and C*-algebras attached to tilings.

scholarly journals Extensions of $ C^*$-algebras by partial isometries

2004 ◽  
Vol 195 (7) ◽  
pp. 951-982 ◽  
Author(s):  
A V Lebedev ◽  
A Odzijewicz
Keyword(s):  
Partial Isometries ◽  
C Algebras

Partial *-Automorphisms, Normalizers, and Submodules in Monotone Complete C*-Algebras

2006 ◽  
Vol 58 (6) ◽  
pp. 1144-1202
Author(s):  
Masamichi Hamana
Keyword(s):  
Automorphism Group ◽  
Inverse Semigroup ◽  
Fundamental Group ◽  
Outer Automorphism ◽  
Type Ii ◽  
Partial Isometries ◽  
Von Neumann ◽  
Outer Automorphism Group ◽  
Linear Subspaces ◽  
C Algebras

AbstractFor monotone complete C*-algebras A ⊂ B with A contained in B as a monotone closed C*-subalgebra, the relation X = AsA gives a bijection between the set of all monotone closed linear subspaces X of B such that AX + XA ⊂ X and XX* + X*X ⊂ A and a set of certain partial isometries s in the “normalizer” of A in B, and similarly for the map s ⟼ Ad s between the latter set and a set of certain “partial *-automorphisms” of A. We introduce natural inverse semigroup structures in the set of such X's and the set of partial *-automorphisms of A, modulo a certain relation, so that the composition of these maps induces an inverse semigroup homomorphism between them. For a large enough B the homomorphism becomes surjective and all the partial *-automorphisms of A are realized via partial isometries in B. In particular, the inverse semigroup associated with a type II1 von Neumann factor, modulo the outer automorphism group, can be viewed as the fundamental group of the factor. We also consider the C*-algebra version of these results.

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