scholarly journals On the Bézout equation in the ring of periodic distributions

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Rudolf Rupp ◽  
Amol Sasane
Keyword(s):  
Polynomial Growth ◽  
Fourier Coefficients ◽  
Type Theorem ◽  
Stable Rank ◽  
Bezout Equation ◽  
Topological Stable Rank

AbstractA corona type theorem is given for the ring D'A(Rd) of periodic distributions in Rd in terms of the sequence of Fourier coefficients of these distributions,which have at most polynomial growth. It is also shown that the Bass stable rank and the topological stable rank of D'A(Rd) are both equal to 1.

scholarly journals On the topological stable rank of non-selfadjoint operator algebras

2007 ◽  
Vol 341 (2) ◽  
pp. 239-253 ◽  
Author(s):  
K. R. Davidson ◽  
R. H. Levene ◽  
L. W. Marcoux ◽  
H. Radjavi
Keyword(s):  
Selfadjoint Operator ◽  
Operator Algebras ◽  
Stable Rank ◽  
Topological Stable Rank

scholarly journals Reduction of topological stable rank in inductive limits ofC∗-algebras

1992 ◽  
Vol 153 (2) ◽  
pp. 267-276 ◽  
Author(s):  
Marius Dadarlat ◽  
Gabriel Nagy ◽  
András Némethi ◽  
Cornel Pasnicu
Keyword(s):  
Stable Rank ◽  
Inductive Limits ◽  
Topological Stable Rank

scholarly journals A note on the topological stable rank of an ideal

2011 ◽  
Vol 139 (11) ◽  
pp. 3999-4002 ◽  
Author(s):  
You Qing Ji ◽  
Yuan Hang Zhang
Keyword(s):  
Stable Rank ◽  
Topological Stable Rank

scholarly journals STABLE RANK FOR INCLUSIONS OF C*-ALGEBRAS

2008 ◽  
Vol 19 (09) ◽  
pp. 1011-1020 ◽  
Author(s):  
HIROYUKI OSAKA
Keyword(s):  
Finite Groups ◽  
Stable Rank ◽  
C Algebra ◽  
C Algebras ◽  
Rank One ◽  
Common Unit ◽  
Topological Stable Rank

When a unital C*-algebra A has topological stable rank one (write tsr (A) = 1), we know that tsr (pAp) = 1 for a non-zero projection p ∈ A. When, however, tsr (A) ≥ 2, it is generally false. We prove that if a unital C*-algebra A has a simple unital C*-subalgebra D of A with common unit such that D has Property (SP) and sup p ∈ P(D) tsr (pAp) < ∞, then tsr (A) ≤ 2. As an application let A be a simple unital C*-algebra with tsr (A) = 1 and Property (SP), [Formula: see text] finite groups, αk actions from Gk to Aut ((⋯((A × α1 G1) ×α2 G2)⋯) ×αk-1 Gk-1). (G0 = {1}). Then [Formula: see text]

The polynomial growth solutions to some sub-elliptic equations on the Heisenberg group

2019 ◽  
Vol 21 (01) ◽  
pp. 1750069 ◽  
Author(s):  
Hairong Liu ◽  
Tian Long ◽  
Xiaoping Yang
Keyword(s):  
Dirichlet Problem ◽  
Heisenberg Group ◽  
Elliptic Equations ◽  
Polynomial Growth ◽  
Bounded Solution ◽  
Type Theorem ◽  
Divergence Form ◽  
Liouville Type ◽  
Periodic Coefficients ◽  
Liouville Type Theorem

We give an explicit description of polynomial growth solutions to some sub-elliptic operators of divergence form with [Formula: see text]-periodic coefficients on the Heisenberg group, where the periodicity has to be meant with respect to the Heisenberg geometry. We show that the polynomial growth solutions are necessarily polynomials with [Formula: see text]-periodic coefficients. We also prove the Liouville-type theorem for the Dirichlet problem to these sub-elliptic equations on an unbounded domain on the Heisenberg group, show that any bounded solution to the Dirichlet problem must be constant.

Jakimovski–Leviatan operators of Kantorovich type involving multiple Appell polynomials

2019 ◽  
Vol 28 (1) ◽  
pp. 73-82 ◽  
Author(s):  
Pooja Gupta ◽  
Ana Maria Acu ◽  
Purshottam Narain Agrawal
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Maximal Function ◽  
Polynomial Growth ◽  
Weighted Space ◽  
Type Theorem ◽  
Degree Of Approximation ◽  
Type Operator ◽  
Appell Polynomials ◽  
Lipschitz Type Maximal Function

Abstract The purpose of the present paper is to obtain the degree of approximation in terms of a Lipschitz type maximal function for the Kantorovich type modification of Jakimovski–Leviatan operators based on multiple Appell polynomials. Also, we study the rate of approximation of these operators in a weighted space of polynomial growth and for functions having a derivative of bounded variation. A Voronvskaja type theorem is obtained. Further, we illustrate the convergence of these operators for certain functions through tables and figures using the Maple algorithm and, by a numerical example, we show that our Kantorovich type operator involving multiple Appell polynomials yields a better rate of convergence than the Durrmeyer type Jakimovski Leviatan operators based on Appell polynomials introduced by Karaisa (2016).

scholarly journals Tracially quasidiagonal extensions and topological stable rank

2003 ◽  
Vol 47 (3) ◽  
pp. 921-937 ◽  
Author(s):  
Huaxin Lin ◽  
Hiroyuki Osaka
Keyword(s):  
Stable Rank ◽  
Topological Stable Rank
Sign in / Sign up

Export Citation Format

Share Document