C*-Algebras of Singular Integral Operators with Shifts Having the Same Nonempty Set of Fixed Points期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

*C-Algebras of Singular Integral Operators with Shifts Having the Same Nonempty Set of Fixed Points**

Authors:	M Amélia Bastos Claudio A Fernandes Yuri I Karlovich

Institution:	(1) Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, P-1049–001 Lisboa, Portugal;(2) Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, P-2825 Monte de Caparica, Portugal;(3) Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Col. Chamilpa, C.P. 62209 Cuernavaca, Morelos, México

Abstract:	The C-subalgebra ${\mathfrak{B}}$ of ${\mathcal{B}}(L^2({\mathbb{T}}))$ generated by all multiplication operators by slowly oscillating and piecewise continuous functions, by the Cauchy singular integral operator and by the range of a unitary representation of an amenable group of diffeomorphisms $g : {\mathbb{T}} \rightarrow {\mathbb{T}}$ with any nonempty set of common fixed points is studied. A symbol calculus for the C-algebra ${\mathfrak{B}}$ and a Fredholm criterion for its elements are obtained. For the C-algebra $\mathcal{A}$ composed by all functional operators in ${\mathfrak{B}}$ , an invertibility criterion for its elements is also established. Both the C-algebras ${\mathfrak{B}}$ and ${\mathcal{A}}$ are investigated by using a generalization of the local-trajectory method for C-algebras associated with C-dynamical systems which is based on the notion of spectral measure. Submitted: April 30, 2007. Accepted: November 5, 2007.

Keywords:	Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 47A53 47G10 47L15 Secondary 47A67 47B33 47L30
本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏