scholarly journals The Fourier–Stieltjes algebra of a C*-dynamical system

2016 ◽  
Vol 27 (06) ◽  
pp. 1650050 ◽  
Author(s):  
Erik Bédos ◽  
Roberto Conti
Keyword(s):  
Dynamical System ◽  
Banach Algebra ◽  
Type Theorem ◽  
Positive Definiteness ◽  
Crossed Product ◽  
System Building ◽  
System A ◽  
Commutative Subalgebras ◽  
Definition Of

In analogy with the Fourier–Stieltjes algebra of a group, we associate to a unital discrete twisted [Formula: see text]-dynamical system a Banach algebra whose elements are coefficients of equivariant representations of the system. Building upon our previous work, we show that this Fourier–Stieltjes algebra embeds continuously in the Banach algebra of completely bounded multipliers of the (reduced or full) [Formula: see text]-crossed product of the system. We introduce a notion of positive definiteness and prove a Gelfand–Raikov type theorem allowing us to describe the Fourier–Stieltjes algebra of a system in a more intrinsic way. We also propose a definition of amenability for [Formula: see text]-dynamical systems and show that it implies regularity. After a study of some natural commutative subalgebras, we end with a characterization of the Fourier–Stieltjes algebra involving [Formula: see text]-correspondences over the (reduced or full) [Formula: see text]-crossed product.

A CONSTRUCTION FOR WEIGHTS ON C*-ALGEBRAS: DUAL WEIGHTS FOR C*-CROSSED PRODUCTS

1999 ◽  
Vol 10 (01) ◽  
pp. 129-157 ◽  
Author(s):  
J. QUAEGEBEUR ◽  
J. VERDING
Keyword(s):  
Dynamical System ◽  
Haar Measure ◽  
Crossed Product ◽  
Crossed Products ◽  
C Algebras ◽  
System A ◽  
Lower Semi ◽  
Continuous Weight ◽  
Densely Defined

A method for constructing densely defined lower semi-continuous weights on C*-algebras is presented. The method can be used to construct a "dual weight" on the C*-crossed product A×αG of a C*-dynamical system (A,G,α), starting from a relatively α-invariant densely defined lower semi-continuous weight on A. As an application we show that the Haar measure on the quantum E(2) group is a C*-dual weight.

Amenability of Lipschitz algebras

1992 ◽  
Vol 112 (3) ◽  
pp. 581-588 ◽  
Author(s):  
Frédéric Gourdeau
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Alternative Definition ◽  
Definition Of

In this article, we study the amenability of Banach algebras in general, and that of Lipschitz algebras in particular. After introducing an alternative definition of amenability, we extend a result of [5], thereby proving a new characterization of amenability for Banach algebras. This characterization relates the amenability of a Banach algebra A to the space of bounded homomorphisms from A into another Banach algebra B (Theorem 4). This result allows us to solve the problem of amenability for virtually all Lipschitz algebras (of complex or Banach algebra valued functions), a class of algebras which has been studied in [2], [4] and [5].

scholarly journals Ideal structure of crossed products by endomorphisms via reversible extensions of C*-dynamical systems

2015 ◽  
Vol 26 (03) ◽  
pp. 1550022 ◽  
Author(s):  
Bartosz Kosma Kwaśniewski
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Transfer Operator ◽  
Crossed Product ◽  
Crossed Products ◽  
Ideal Structure ◽  
Gauge Invariant ◽  
C Algebra ◽  
System A ◽  
The Ideal

We consider an extendible endomorphism α of a C*-algebra A. We associate to it a canonical C*-dynamical system (B, β) that extends (A, α) and is "reversible" in the sense that the endomorphism β admits a unique regular transfer operator β⁎. The theory for (B, β) is analogous to the theory of classic crossed products by automorphisms, and the key idea is to describe the counterparts of classic notions for (B, β) in terms of the initial system (A, α). We apply this idea to study the ideal structure of a non-unital version of the crossed product C*(A, α, J) introduced recently by the author and A. V. Lebedev. This crossed product depends on the choice of an ideal J in (ker α)⊥, and if J = ( ker α)⊥ it is a modification of Stacey's crossed product that works well with non-injective α's. We provide descriptions of the lattices of ideals in C*(A, α, J) consisting of gauge-invariant ideals and ideals generated by their intersection with A. We investigate conditions under which these lattices coincide with the set of all ideals in C*(A, α, J). In particular, we obtain simplicity criteria that besides minimality of the action require either outerness of powers of α or pointwise quasinilpotence of α.

BIRKHOFF SPECTRA FOR ONE-DIMENSIONAL MAPS WITH SOME HYPERBOLICITY

2010 ◽  
Vol 10 (01) ◽  
pp. 53-75 ◽  
Author(s):  
YONG MOO CHUNG
Keyword(s):  
Dynamical System ◽  
Hausdorff Dimension ◽  
Multifractal Analysis ◽  
Probability Measures ◽  
One Dimensional ◽  
System A ◽  
Topologically Mixing ◽  
One Dimensional Maps ◽  
Dimension One

We study the multifractal analysis for smooth dynamical systems in dimension one. It is given a characterization of the Hausdorff dimension of the level set obtained from the Birkhoff averages of a continuous function by the local dimensions of hyperbolic measures for a topologically mixing C2 map modeled by an abstract dynamical system. A characterization which corresponds to above is also given for the ergodic basins of invariant probability measures. And it is shown that the complement of the set of quasi-regular points carries full Hausdorff dimension.

Neurochemistry of L-Glutamate Transport in the CNS: A Review of Thirty Years of Progress

2001 ◽  
Vol 66 (9) ◽  
pp. 1315-1340 ◽  
Author(s):  
Vladimir J. Balcar ◽  
Akiko Takamoto ◽  
Yukio Yoneda
Keyword(s):  
Molecular Biology ◽  
Glutamate Transport ◽  
Mammalian Brain ◽  
Activity Data ◽  
System A ◽  
Recent Developments ◽  
The Central Nervous System ◽  
Health And Disease ◽  
Disease Analysis

The review highlights the landmark studies leading from the discovery and initial characterization of the Na+-dependent "high affinity" uptake in the mammalian brain to the cloning of individual transporters and the subsequent expansion of the field into the realm of molecular biology. When the data and hypotheses from 1970's are confronted with the recent developments in the field, we can conclude that the suggestions made nearly thirty years ago were essentially correct: the uptake, mediated by an active transport into neurons and glial cells, serves to control the extracellular concentrations of L-glutamate and prevents the neurotoxicity. The modern techniques of molecular biology may have provided additional data on the nature and location of the transporters but the classical neurochemical approach, using structural analogues of glutamate designed as specific inhibitors or substrates for glutamate transport, has been crucial for the investigations of particular roles that glutamate transport might play in health and disease. Analysis of recent structure/activity data presented in this review has yielded a novel insight into the pharmacological characteristics of L-glutamate transport, suggesting existence of additional heterogeneity in the system, beyond that so far discovered by molecular genetics. More compounds that specifically interact with individual glutamate transporters are urgently needed for more detailed investigations of neurochemical characteristics of glutamatergic transport and its integration into the glutamatergic synapses in the central nervous system. A review with 162 references.

Inverse problems for finite Jacobi matrices and Krein–Stieltjes strings

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Mikhaylov ◽  
Victor Mikhaylov
Keyword(s):  
Dynamical System ◽  
Inverse Problems ◽  
Jacobi Matrix ◽  
Jacobi Matrices ◽  
Unknown Parameters ◽  
Stieltjes String ◽  
Propagation Of Waves ◽  
Dynamic Inverse

Abstract We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein–Stieltjes string. We offer three methods of recovering unknown parameters: entries of a Jacobi matrix in the first problem and point masses and distances between them in the second, from dynamic Dirichlet-to-Neumann operators. We also answer a question on a characterization of dynamic inverse data for these two problems.

scholarly journals Experimental Evaluation of Shear Behavior of Stone Masonry Wall

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2313
Author(s):  
Maria Luisa Beconcini ◽  
Pietro Croce ◽  
Paolo Formichi ◽  
Filippo Landi ◽  
Benedetta Puccini
Keyword(s):  
Shear Behavior ◽  
Stone Masonry ◽  
Masonry Walls ◽  
Mechanical Parameters ◽  
In Situ Tests ◽  
Capacity Curves ◽  
Historical Structures ◽  
Definition Of

The evaluation of the shear behavior of masonry walls is a first fundamental step for the assessment of existing masonry structures in seismic zones. However, due to the complexity of modelling experimental behavior and the wide variety of masonry types characterizing historical structures, the definition of masonry’s mechanical behavior is still a critical issue. Since the possibility to perform in situ tests is very limited and often conflicting with the needs of preservation, the characterization of shear masonry behavior is generally based on reference values of mechanical properties provided in modern structural codes for recurrent masonry categories. In the paper, a combined test procedure for the experimental characterization of masonry mechanical parameters and the assessment of the shear behavior of masonry walls is presented together with the experimental results obtained on three stone masonry walls. The procedure consists of a combination of three different in situ tests to be performed on the investigated wall. First, a single flat jack test is executed to derive the normal compressive stress acting on the wall. Then a double flat jack test is carried out to estimate the elastic modulus. Finally, the proposed shear test is performed to derive the capacity curve and to estimate the shear modulus and the shear strength. The first results obtained in the experimental campaign carried out by the authors confirm the capability of the proposed methodology to assess the masonry mechanical parameters, reducing the uncertainty affecting the definition of capacity curves of walls and consequently the evaluation of seismic vulnerability of the investigated buildings.

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