scholarly journals Frobenius C∗-algebras and local adjunctions of C∗-correspondences

2021 ◽  
Author(s):  
Tyrone Crisp
Keyword(s):  
Prior Work ◽  
C Algebras ◽  
Frobenius Algebras ◽  
Standard Notion ◽  
One To One

Generalizing the well-known correspondence between two-sided adjunctions and Frobenius algebras, we establish a one-to-one correspondence between local adjunctions of [Formula: see text]-correspondences, as defined and studied in prior work with Clare and Higson; and Frobenius [Formula: see text]-algebras, a natural [Formula: see text]-algebraic adaptation of the standard notion of Frobenius algebras that we introduce here.

Discrete coactions on Hilbert C*-modules

1996 ◽  
Vol 119 (1) ◽  
pp. 103-112
Author(s):  
Chi-Keung Ng
Keyword(s):  
Crossed Products ◽  
C Algebras ◽  
One To One

In this paper, we will investigate discrete coactions on Hilbert C*-modules. In particular, we obtain a one-to-one correspondence between Hilbert C*-modules with discrete coactions and Hilbert C*-modules over the crossed products of the original C*-algebras which satisfies some nice properties (see 3·6 and 3·7). Then we will give some applications of this correspondence in the last three sections.In Section 2, we give some results about discrete coactions on Hilbert C*-modules which mainly correspond to those about discrete coactions on C*-algebras (see [7]).

C*-ALGEBRAS OF TRIVIAL K-THEORY AND SEMILATTICES

1999 ◽  
Vol 10 (01) ◽  
pp. 93-128 ◽  
Author(s):  
HUAXIN LIN
Keyword(s):  
Direct Limit ◽  
Tensor Products ◽  
Equivalence Classes ◽  
Direct Sums ◽  
C Algebras ◽  
Direct Limits ◽  
One To One ◽  
K Theory ◽  
Essential Extensions ◽  
Distributive Semilattices

We give a class of nuclear C*-algebras which contains [Formula: see text] and is closed under stable isomorphism, ideals, quotients, hereditary subalgebras, tensor products, direct sums, direct limits as well as extensions. We show that this class of C*-algebras is classified by their equivalence classes of projections and there is a one to one correspondence between (unital) C*-algebras in the class and countable distributive semilattices (with largest elements). One of the main results is that essential extensions of a C*-algebras which is a direct limit of finite direct sums of corners of [Formula: see text] by the same type of C*-algebras are still direct limits of finite direct sums of corners of [Formula: see text].

The ideal structures of self-similar -graph C*-algebras

2020 ◽  
pp. 1-28
Author(s):  
HUI LI ◽  
DILIAN YANG
Keyword(s):  
Gauge Invariant ◽  
C Algebra ◽  
C Algebras ◽  
Primitive Ideals ◽  
Vertex Set ◽  
Self Similar ◽  
One To One ◽  
The Ideal ◽  
The Way

Let $(G,\unicode[STIX]{x1D6EC})$ be a self-similar $k$ -graph with a possibly infinite vertex set $\unicode[STIX]{x1D6EC}^{0}$ . We associate a universal C*-algebra ${\mathcal{O}}_{G,\unicode[STIX]{x1D6EC}}$ to $(G,\unicode[STIX]{x1D6EC})$ . The main purpose of this paper is to investigate the ideal structures of ${\mathcal{O}}_{G,\unicode[STIX]{x1D6EC}}$ . We prove that there exists a one-to-one correspondence between the set of all $G$ -hereditary and $G$ -saturated subsets of $\unicode[STIX]{x1D6EC}^{0}$ and the set of all gauge-invariant and diagonal-invariant ideals of ${\mathcal{O}}_{G,\unicode[STIX]{x1D6EC}}$ . Under some conditions, we characterize all primitive ideals of ${\mathcal{O}}_{G,\unicode[STIX]{x1D6EC}}$ . Moreover, we describe the Jacobson topology of some concrete examples, which includes the C*-algebra of the product of odometers. On the way to our main results, we study self-similar $P$ -graph C*-algebras in depth.

A Support Program

1994 ◽  
Vol 25 (2) ◽  
pp. 112-114 ◽  
Author(s):  
Henna Grunblatt ◽  
Lisa Daar
Keyword(s):  
Hearing Aids ◽  
School Counselor ◽  
Support Program ◽  
Educational Audiology ◽  
Part Program ◽  
One To One

A program for providing information to children who are deaf about their deafness and addressing common concerns about deafness is detailed. Developed by a school audiologist and the school counselor, this two-part program is geared for children from 3 years to 15 years of age. The first part is an educational audiology program consisting of varied informational classes conducted by the audiologist. Five topics are addressed in this part of the program, including basic audiology, hearing aids, FM systems, audiograms, and student concerns. The second part of the program consists of individualized counseling. This involves both one-to-one counseling sessions between a student and the school counselor, as well as conjoint sessions conducted—with the student’s permission—by both the audiologist and the school counselor.

An Introduction to K-Theory for C*-Algebras

2000 ◽  
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
C Algebras ◽  
K Theory

Review of One to One: The Experience of Psychotherapy.

1989 ◽  
Vol 34 (10) ◽  
pp. 958-958
Author(s):  
No authorship indicated
Keyword(s):  
One To One

Influence of Rim Run-Out on the Nonuniformity of Tire-Wheel Assemblies

1994 ◽  
Vol 22 (2) ◽  
pp. 99-120 ◽  
Author(s):  
T. B. Rhyne ◽  
R. Gall ◽  
L. Y. Chang
Keyword(s):  
Finite Element ◽  
Radial Force ◽  
Membrane Model ◽  
Model Experiments ◽  
Force Variation ◽  
One To One ◽  
The One

Abstract An analytical membrane model is used to study how wheel imperfections are converted into radial force variation of the tire-wheel assembly. This model indicates that the radial run-out of the rim generates run-out of the tire-wheel assembly at slightly less than the one to one ratio that was expected. Lateral run-out of the rim is found to generate radial run-out of the tire-wheel assembly at a ratio that is dependent on the tire design and the wheel width. Finite element studies of a production tire validate and quantify the results of the membrane model. Experiments using a specially constructed precision wheel demonstrate the behavior predicted by the models. Finally, a population of production tires and wheels show that the lateral run-out of the rims contribute a significant portion to the assembly radial force variation. These findings might be used to improve match-mounting results by taking lateral rim run-out into account.

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