Positive Definite Bounded Matrices and a Characterization of Amenable Groups

1985 ◽  
Vol 95 (3) ◽  
pp. 357 ◽  
Author(s):  
Marek Bozejko
Keyword(s):  
Positive Definite ◽  
Amenable Groups ◽  
Bounded Matrices

scholarly journals Positive Definite Norm Dependent Matrices In Stochastic Modeling

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
Sebastian P. Kuniewski ◽  
Jolanta K. Misiewicz
Keyword(s):  
Stochastic Modeling ◽  
Mathematical Analysis ◽  
Spatial Data ◽  
Correlation Matrix ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Necessary Condition ◽  
The Family ◽  
Definite Correlation

AbstractPositive definite norm dependent matrices are of interest in stochastic modeling of distance/norm dependent phenomena in nature. An example is the application of geostatistics in geographic information systems or mathematical analysis of varied spatial data. Because the positive definiteness is a necessary condition for a matrix to be a valid correlation matrix, it is desirable to give a characterization of the family of the distance/norm dependent functions that form a valid (positive definite) correlation matrix. Thus, the main reason for writing this paper is to give an overview of characterizations of norm dependent real functions and consequently norm dependent matrices, since this information is somehow hidden in the theory of geometry of Banach spaces

Free group C*-algebras associated with ℓp

2014 ◽  
Vol 25 (07) ◽  
pp. 1450065 ◽  
Author(s):  
Rui Okayasu
Keyword(s):  
Free Group ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Linear Functionals ◽  
C Algebra ◽  
Tracial State ◽  
C Algebras ◽  
Positive Linear Functionals ◽  
The Ideal

For every p ≥ 2, we give a characterization of positive definite functions on a free group with finitely many generators, which can be extended to positive linear functionals on the free group C*-algebra associated with the ideal ℓp. This is a generalization of Haagerup's characterization for the case of the reduced free group C*-algebra. As a consequence, the canonical quotient map between the associated C*-algebras is not injective, and they have a unique tracial state.

On graph products of multipliers and the Haagerup property for -dynamical systems

2019 ◽  
Vol 40 (12) ◽  
pp. 3188-3216
Author(s):  
SCOTT ATKINSON
Keyword(s):  
Dynamical Systems ◽  
Positive Definite ◽  
Alternative Proof ◽  
Discrete Groups ◽  
Graph Products ◽  
Graph Product ◽  
Haagerup Property ◽  
Products Of Groups ◽  
Product Action

We consider the notion of the graph product of actions of discrete groups $\{G_{v}\}$ on a $C^{\ast }$-algebra ${\mathcal{A}}$ and show that under suitable commutativity conditions the graph product action $\star _{\unicode[STIX]{x1D6E4}}\unicode[STIX]{x1D6FC}_{v}:\star _{\unicode[STIX]{x1D6E4}}G_{v}\curvearrowright {\mathcal{A}}$ has the Haagerup property if each action $\unicode[STIX]{x1D6FC}_{v}:G_{v}\curvearrowright {\mathcal{A}}$ possesses the Haagerup property. This generalizes the known results on graph products of groups with the Haagerup property. To accomplish this, we introduce the graph product of multipliers associated to the actions and show that the graph product of positive-definite multipliers is positive definite. These results have impacts on left-transformation groupoids and give an alternative proof of a known result for coarse embeddability. We also record a cohomological characterization of the Haagerup property for group actions.

scholarly journals POSITIVE ENERGY REPRESENTATIONS AND CONTINUITY OF PROJECTIVE REPRESENTATIONS FOR GENERAL TOPOLOGICAL GROUPS

2013 ◽  
Vol 56 (2) ◽  
pp. 295-316 ◽  
Author(s):  
KARL-HERMANN NEEB
Keyword(s):  
Positive Definite ◽  
Unitary Representations ◽  
Positive Energy ◽  
Topological Groups ◽  
Negative Spectrum ◽  
Continuous Action ◽  
Projective Representations ◽  
Irreducible Unitary Representations ◽  
The One

AbstractLetGandTbe topological groups, α :T→ Aut(G) a homomorphism defining a continuous action ofTonGandG♯:=G⋊αTthe corresponding semidirect product group. In this paper, we address several issues concerning irreducible continuous unitary representations (π♯,${\mathcal{H}}$) ofG♯whose restriction toGremains irreducible. First, we prove that, forT=${\mathbb R}$, this is the case for any irreducible positive energy representation ofG♯, i.e. for which the one-parameter groupUt:= π♯(1,t) has non-negative spectrum. The passage from irreducible unitary representations ofGto representations ofG♯requires that certain projective unitary representations are continuous. To facilitate this verification, we derive various effective criteria for the continuity of projective unitary representations. Based on results of Borchers forW*-dynamical systems, we also derive a characterization of the continuous positive definite functions onGthat extend toG♯.

Graphical characterization of positive definite non symmetric quasi-Cartan matrices

2018 ◽  
Vol 341 (5) ◽  
pp. 1215-1224 ◽  
Author(s):  
Claudia Pérez ◽  
Daniel Rivera
Keyword(s):  
Positive Definite ◽  
Cartan Matrices

scholarly journals Diagonal entries of the combined matrix of sign regular matrices of order three

2021 ◽  
Vol 40 (1) ◽  
pp. 255-271
Author(s):  
Maria T. Gassó ◽  
Iván Gil ◽  
Isabel Giménez ◽  
Máximo Santana ◽  
Elaine Segura
Keyword(s):  
Positive Definite ◽  
Nonsingular Matrix ◽  
Positive Definite Matrices ◽  
Totally Positive ◽  
Combined Matrix

The study of the diagonal entries of the combined matrix of a nonsingular matrix A has been considered by different authors for the classes of M—matrices, positive definite matrices and totally positive (negative) matrices. This problem appears to be difficult as the results have been done only for matrices of order three. In this work, we continue to give the characterization of the diagonal entries of the combined matrix of the remainder sign regular matrices. Thus, the problem is closed for all possible sign regular matrices of order three.

Sign in / Sign up

Export Citation Format

Share Document