Quasi-standard C*-algebras

1990 ◽  
Vol 107 (2) ◽  
pp. 349-360 ◽  
Author(s):  
R. J. Archbold ◽  
D. W. B. Somerset
Keyword(s):  
Cross Sections ◽  
Equivalence Relation ◽  
Dense Subset ◽  
Base Space ◽  
Ideal Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
C Algebras ◽  
Necessary And Sufficient ◽  
Full Algebra

AbstactA necessary and sufficient condition is given for a separable C*-algebra to be *-isomorphic to a maximal full algebra of cross-sections over a base space such that the fibre algebras are primitive throughout a dense subset. The condition is that the relation of inseparability for pairs of points in the primitive ideal space should be an open equivalence relation.

Minimal primal ideal spaces and norms of inner derivations of tensor products of C*-algebras

1996 ◽  
Vol 119 (2) ◽  
pp. 297-308 ◽  
Author(s):  
Eberhard Kaniuth
Keyword(s):  
Cross Sections ◽  
Dense Subset ◽  
Tensor Products ◽  
The Other ◽  
Primitive Ideal ◽  
Ideal Space ◽  
C Algebra ◽  
C Algebras ◽  
Other Hand ◽  
Full Algebra

An ideal I in a C*-algebra A is called primal if whenever n ≥ 2 and J1,…, Jn are ideals in A with zero product then Jk ⊆ I for at least one k. The topologized space of minimal primal ideals of A, Min-Primal (A), has been extensively studied by Archbold[3]. Very much in the spirit of Fell's work [14] it was shown in [3, theorem 5·3] (see also [5, theorem 3·4]) that if A is quasi-standard, then A is *-isomorphic to a maximal full algebra of cross-sections of Min-Primal (A). Moreover, if A is separable the fibre algebras are primitive throughout a dense subset. On the other hand, the complete regularization of the primitive ideal space of A gives rise to the space of so-called Glimm ideals of A, Glimm (A). It turned out that A is quasi-standard exactly when Min-Primal (A) and Glimm (A) coincide as sets and topologically [5, theorem 3·3].

Horodeckis criterion of separability of mixed states in von Neumann and C*-algebras

2014 ◽  
Vol 17 (04) ◽  
pp. 1450028 ◽  
Author(s):  
Marek Miller ◽  
Robert Olkiewicz
Keyword(s):  
Quantum Systems ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Mixed States ◽  
Von Neumann ◽  
C Algebras ◽  
Necessary And Sufficient

The Horodeckis necessary and sufficient condition of separability of mixed states is generalized to arbitrary composite quantum systems.

scholarly journals (1, 2) AND WEAK (1, 3) HOMOTOPIES ON KNOT PROJECTIONS

2013 ◽  
Vol 22 (14) ◽  
pp. 1350085 ◽  
Author(s):  
NOBORU ITO ◽  
YUSUKE TAKIMURA
Keyword(s):  
Equivalence Relation ◽  
Finite Sequence ◽  
Reidemeister Move ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Homotopy Classes ◽  
The Third ◽  
Reidemeister Moves ◽  
Necessary And Sufficient

In this paper, we obtain the necessary and sufficient condition that two knot projections are related by a finite sequence of the first and second flat Reidemeister moves (Theorem 2.2). We also consider an equivalence relation that is called weak (1, 3) homotopy. This equivalence relation occurs by the first flat Reidemeister move and one of the third flat Reidemeister moves. We introduce a map sending weak (1, 3) homotopy classes to knot isotopy classes (Sec. 3). Using the map, we determine which knot projections are trivialized under weak (1, 3) homotopy (Corollary 4.1).

scholarly journals Quotient supermanifolds

1998 ◽  
Vol 58 (1) ◽  
pp. 107-120 ◽  
Author(s):  
Claudio Bartocci ◽  
Ugo Bruzzo ◽  
Daniel Hernández Ruipérez ◽  
Vladimir Pestov
Keyword(s):  
Equivalence Relation ◽  
Smooth Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

A necessary and sufficient condition for the existence of a supermanifold structure on a quotient defined by an equivalence relation is established. Furthermore, we show that an equivalence relation R on a Berezin-Leĭtes-Kostant supermanifold X determines a quotient supermanifold X/R if and only if the restriction R0 of R to the underlying smooth manifold X0 of X determines a quotient smooth manifold X0/R0.

Discontinuous homomorphisms from C*-algebras

1991 ◽  
Vol 110 (1) ◽  
pp. 147-150 ◽  
Author(s):  
D. W. B. Somerset
Keyword(s):  
Banach Algebra ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
C Algebra ◽  
C Algebras ◽  
Necessary And Sufficient

AbstractA necessary and sufficient condition is given for a unital C*-algebra A to admit a discontinuous homomorphism into a Banach algebra which is continuous on its centre. The condition is that A must have a Glimm ideal G such that the C*-algebra A/G admits a discontinuous homomorphism into a Banach algebra.

scholarly journals ON THE STRUCTURE OF SOME REDUCED AMALGAMATED FREE PRODUCT C*-ALGEBRAS

2011 ◽  
Vol 22 (02) ◽  
pp. 281-306 ◽  
Author(s):  
NIKOLAY A. IVANOV
Keyword(s):  
Free Product ◽  
Sufficient Conditions ◽  
Positive Cone ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Free Products ◽  
C Algebras ◽  
Amalgamated Free Product ◽  
Necessary And Sufficient

We study some reduced free products of C*-algebras with amalgamations. We give sufficient conditions for the positive cone of the K0 group to be the largest possible. We also give sufficient conditions for simplicity and uniqueness of trace. We use the latter result to give a necessary and sufficient condition for simplicity and uniqueness of trace of the reduced C*-algebras of the Baumslag–Solitar groups BS(m, n).

Characterizing rosy theories

2007 ◽  
Vol 72 (3) ◽  
pp. 919-940 ◽  
Author(s):  
Clifton Ealy ◽  
Alf Onshuus
Keyword(s):  
Equivalence Relation ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Rosy Theories ◽  
Relation Rank

AbstractWe examine several conditions, either the existence of a rank or a particular property of þ-forking that suggest the existence of a well-behaved independence relation, and determine the consequences of each of these conditions towards the rosiness of the theory. In particular we show that the existence of an ordinal valued equivalence relation rank is a (necessary and) sufficient condition for rosiness.

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 C*-Algebras of Irreversible Dynamical Systems

2006 ◽  
Vol 58 (1) ◽  
pp. 39-63 ◽  
Author(s):  
R. Exel ◽  
A. Vershik
Keyword(s):  
Measure Space ◽  
General Theorem ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Circle Actions ◽  
Generators And Relations ◽  
C Algebras ◽  
Special Cases ◽  
Measure Preserving Transformation ◽  
Necessary And Sufficient

AbstractWe show that certain C*-algebras which have been studied by, among others, Arzumanian, Vershik, Deaconu, and Renault, in connection with a measure-preserving transformation of a measure space or a covering map of a compact space, are special cases of the endomorphism crossed product construction recently introduced by the first named author. As a consequence these algebras are given presentations in terms of generators and relations. These results come as a consequence of a general theorem on faithfulness of representations which are covariant with respect to certain circle actions. For the case of topologically free covering maps we prove a stronger result on faithfulness of representations which needs no covariance. We also give a necessary and sufficient condition for simplicity.

scholarly journals Derivations on some (possibly non-separable) C*-algebras

1981 ◽  
Vol 22 (1) ◽  
pp. 43-56 ◽  
Author(s):  
J. P. Sproston
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Degree ◽  
C Algebras ◽  
Direct Sum ◽  
Necessary And Sufficient

In an important recent paper [4], G. A. Elliott has given a necessary and sufficient condition for every derivation on a separable C*-algebra with identity to be inner. Indeed, Elliott's condition has since been shown, by Akemann and Pedersen, to be equivalent to the C*-algebra being a finite direct sum of C*-algebras which are either homogeneous of finite degree or simple [8, Corollary 3.10].

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