scholarly journals HILBERT C*-BIMODULES OF FINITE INDEX AND APPROXIMATION PROPERTIES OF C*-ALGEBRAS

2017 ◽  
Vol 60 (2) ◽  
pp. 321-331
Author(s):  
MARZIEH FOROUGH ◽  
MASSOUD AMINI
Keyword(s):  
Finite Index ◽  
Morita Equivalence ◽  
Discrete Groups ◽  
Crossed Products ◽  
Approximation Properties ◽  
C Algebras ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
The Stability

AbstractLet A and B be arbitrary C*-algebras, we prove that the existence of a Hilbert A–B-bimodule of finite index ensures that the WEP, QWEP, and LLP along with other finite-dimensional approximation properties such as CBAP and (S)OAP are shared by A and B. For this, we first study the stability of the WEP, QWEP, and LLP under Morita equivalence of C*-algebras. We present examples of Hilbert A–B-bimodules, which are not of finite index, while such properties are shared between A and B. To this end, we study twisted crossed products by amenable discrete groups.

scholarly journals $K$-Continuity Is Equivalent To $K$-Exactness

2016 ◽  
Vol 118 (1) ◽  
pp. 95
Author(s):  
Otgonbayar Uuye
Keyword(s):  
Tensor Product ◽  
Approximation Theory ◽  
Inductive Limits ◽  
C Algebra ◽  
C Algebras ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation

Let $A$ be a $C^{*}$-algebra. It is well known that the functor $B \mapsto A \otimes B$ of taking the minimal tensor product with $A$ preserves inductive limits if and only if it is exact. $C^{*}$-algebras with this property play an important role in the structure and finite-dimensional approximation theory of $C^{*}$-algebras. We consider a $K$-theoretic analogue of this result and show that the functor $B \mapsto K_{0}(A \otimes B)$ preserves inductive limits if and only if it is half-exact.

Finite-dimensional approximation of the scattering matrix

1986 ◽  
Vol 64 (5) ◽  
pp. 611-616 ◽  
Author(s):  
Helmut Kröger ◽  
Anais Smailagic ◽  
Ralph Girard
Keyword(s):  
Weak Coupling ◽  
Weak Coupling Regime ◽  
S Wave ◽  
Proton Proton ◽  
Time Evolution Operator ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
S Matrix ◽  
Computer Calculations

A finite-dimensional nonperturbative approximation scheme of the time-evolution operator and the S matrix for relativistic field theories is discussed. It is amenable to computer calculations. Parallels with lattice-field theory are drawn. The method is outlined for the ϕ4 theory. Equivalence to standard perturbation theory in the weak-coupling regime is obtained in the limit of the approximation parameters. The method is tested numerically for nonrelativistic proton–proton s-wave scattering and the the ϕ4 model in the weak-coupling regime in 1 + 1 dimensions. In both examples, convergence to the reference solution is found.

An Approach to Acoustic Noise Control via Passivity Techniques

2001 ◽  
Author(s):  
A. G. Kelkar ◽  
Suresh M. Joshi
Keyword(s):  
Design Methodology ◽  
Controller Design ◽  
Acoustic Noise ◽  
Broad Band ◽  
Resonant Mode ◽  
Robust Controller ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Guaranteed Stability ◽  
Dimensional Approximation

Abstract This paper presents a passivity-based robust controller design methodology for broad-band control of acoustic noise in ducts. A brief review of passivity-based control using passification techniques is given for non-passive dynamic systems. An application of this design technique to the acoustic duct system is presented. The acoustic duct model being inherently non-passive, passification techniques are necessary to render the system passive. The controller design is based on finite-dimensional approximation and is shown to be robust to unmodeled dynamics and parametric uncertainties. The control design methodology exploits inherent robustness of passivity-based controllers and selective mode attenuation capability of resonant mode controllers. The resulting controller is low-order, robust, broadband, and has guaranteed stability.

Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data

2020 ◽  
Vol 20 (1) ◽  
pp. 109-120 ◽  
Author(s):  
Suzhen Jiang ◽  
Kaifang Liao ◽  
Ting Wei
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Fractional Diffusion ◽  
Initial Value ◽  
Diffusion Wave ◽  
One Dimensional ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
Continuation Technique

AbstractIn this study, we consider an inverse problem of recovering the initial value for a multi-dimensional time-fractional diffusion-wave equation. By using some additional boundary measured data, the uniqueness of the inverse initial value problem is proven by the Laplace transformation and the analytic continuation technique. The inverse problem is formulated to solve a Tikhonov-type optimization problem by using a finite-dimensional approximation. We test four numerical examples in one-dimensional and two-dimensional cases for verifying the effectiveness of the proposed algorithm.

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