On the contractability of the unitary group of the Hilbert space over a C⋆-algebra

1982 ◽  
Vol 5 (1) ◽  
pp. 888-891 ◽  
Author(s):  
James A. Mingo
Keyword(s):  
Hilbert Space ◽  
Unitary Group ◽  
C Algebra

scholarly journals Construction and pure infiniteness of $C^*$-algebras associated with lambda-graph systems

2005 ◽  
Vol 97 (1) ◽  
pp. 73 ◽  
Author(s):  
Kengo Matsumoto
Keyword(s):  
Hilbert Space ◽  
Bratteli Diagram ◽  
C Algebra ◽  
C Algebras ◽  
Shift Transformation ◽  
Labeled Graphs ◽  
Graph System ◽  
Creation Operators

A $\lambda$-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. In [16] the author has introduced a $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ associated with a $\lambda$-graph system $\mathfrak{L}$ by using groupoid method as a generalization of the Cuntz-Krieger algebras. In this paper, we concretely construct the $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ by using both creation operators and projections on a sub Fock Hilbert space associated with $\mathfrak{L}$. We also introduce a new irreducible condition on $\mathfrak{L}$ under which the $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ becomes simple and purely infinite.

On the “Third Definition” of the Topology on the Spectrum of a C*-Algebra

1971 ◽  
Vol 23 (3) ◽  
pp. 445-450 ◽  
Author(s):  
L. Terrell Gardner
Keyword(s):  
Hilbert Space ◽  
Quotient Space ◽  
Principal Result ◽  
Irreducible Representations ◽  
C Algebra ◽  
Fell Topology ◽  
The Third ◽  
Definition Of ◽  
Image Position

0. In [3], Fell introduced a topology on Rep (A,H), the collection of all non-null but possibly degenerate *-representations of the C*-algebra A on the Hilbert space H. This topology, which we will call the Fell topology, can be described by giving, as basic open neighbourhoods of π0 ∈ Rep(A, H), sets of the formwhere the ai ∈ A, and the ξj ∈ H(π0), the essential space of π0 [4].A principal result of [3, Theorem 3.1] is that if the Hilbert dimension of H is large enough to admit all irreducible representations of A, then the quotient space Irr(A, H)/∼ can be identified with the spectrum (or “dual“) Â of A, in its hull-kernel topology.

THE TRACE SPACE INVARIANT AND UNITARY GROUP OF C*-ALGEBRA

2003 ◽  
Vol 24 (01) ◽  
pp. 115-122
Author(s):  
XIAOCHUN FANG
Keyword(s):  
Unitary Group ◽  
C Algebra ◽  
Trace Space

THE REPRESENTATIONS AND ENDOMORPHISMS OF A SEPARABLE NUCLEAR C*-ALGEBRA

2003 ◽  
Vol 14 (03) ◽  
pp. 313-326 ◽  
Author(s):  
AKITAKA KISHIMOTO
Keyword(s):  
Hilbert Space ◽  
Irreducible Representation ◽  
Separable Hilbert Space ◽  
Type I ◽  
C Algebra

It is shown that if A is a separable, non-type I, nuclear simple C*-algebra and π is an irreducible representation of A, then for any representation ρ on a separable Hilbert space of A there is an endomorphism α of A such that ρ is unitarily equivalent to πα.

Extreme Points of the Convex set of Stochastic Maps on A C*-Algebra

1998 ◽  
Vol 01 (04) ◽  
pp. 599-609 ◽  
Author(s):  
K. R. Parthasarathy
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Convex Set ◽  
Convex Combination ◽  
Extreme Points ◽  
Bounded Operators ◽  
Completely Positive ◽  
C Algebra ◽  
Permutation Matrices ◽  
Normal Maps

Let [Formula: see text] be a unital C*-subalgebra of the C*-algebra ℬ(ℋ) of all bounded operators on a complex separable Hilbert space ℋ. Let [Formula: see text] denote the convex set of all unital, linear, completely positive and normal maps of [Formula: see text] into itself. Using Stinespring's theorem, we present a criterion for an element [Formula: see text] to be extremal. When [Formula: see text], this criterion leads to an explicit description of the set of all extreme points of [Formula: see text]. We also obtain a quantum probabilistic analogue of the classical Birkhoff's theorem2 that every bistochastic matrix can be expressed as a convex combination of permutation matrices.

scholarly journals FORKING AND STABILITY IN THE REPRESENTATIONS OF A C*-ALGEBRA

2015 ◽  
Vol 80 (3) ◽  
pp. 785-796
Author(s):  
CAMILO ARGOTY
Keyword(s):  
Hilbert Space ◽  
C Algebra ◽  
Image Position

AbstractWe show that the theory of a nondegenerate representation of a C*-algebra ${\cal A}$ over a Hilbert space H is superstable. Also, we characterize forking, orthogonality and domination of types.

scholarly journals The irreducibility of C*-algebras acting on Hilbert C*-modules

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2425-2433
Author(s):  
Runliang Jiang
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Compact Operators ◽  
C Algebra ◽  
C Algebras ◽  
The Difference

Let B be a C*-algebra, E be a Hilbert B module and L(E) be the set of adjointable operators on E. Let A be a non-zero C*-subalgebra of L(E). In this paper, some new kinds of irreducibilities of A acting on E are introduced, which are all the generalizations of those associated to Hilbert spaces. The difference between these irreducibilities are illustrated by a number of counterexamples. It is concluded that for a full Hilbert B-module, these irreducibilities are all equivalent if and only if the underlying C*-algebra B is isomorphic to the C*-algebra of all compact operators on a Hilbert space.

scholarly journals GENERALIZED JENSEN’S EQUATIONS IN BANACH MODULES OVER A C∗-ALGEBRA AND ITS UNITARY GROUP

2003 ◽  
Vol 7 (4) ◽  
pp. 641-655 ◽  
Author(s):  
Deok-Hoon Boo ◽  
Sei-Qwon Oh ◽  
Chun-Gil Park ◽  
Jae-Myung Park
Keyword(s):  
Unitary Group ◽  
C Algebra ◽  
Banach Modules
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