A C*-algebra of singular integral operators with shifts admitting distinct fixed points

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:413

Article

Bastos, M. A.¹  Fernandes, C. A.²  Karlovich, Yu. I.³ 

[1] Inst Super Tecn, Dept Matemat, P-1049001 Lisbon, Portugal

[2] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, P-2825 Monte De Caparica, Portugal

[3] Univ Autonoma Estado Morelos, Fac Ciencias, Cuernavaca 62209, Morelos, Mexico

关键词: Singular integral operator with shifts;    Piecewise slowly oscillating function;    C*-algebra;    Faithful representation;    Fredholmness;   

DOI  :  10.1016/j.jmaa.2013.12.001

来源: Elsevier

【 摘 要 】

Representations on Hilbert spaces for a nonlocal C*-algebra B of singular integral operators with piecewise slowly oscillating coefficients extended by a group of unitary shift operators are constructed. The group of unitary shift operators U-g in the C*-algebra B is associated with a discrete amenable group G of orientation-preserving piecewise smooth homeomorphisms g : T -> T that acts topologically freely on T and admits distinct fixed points for different shifts. A C*-algebra isomorphism of the quotient C*-algebra B/K, where K is the ideal of compact operators, onto a C*-algebra of Fredholm symbols is constructed by applying the local-trajectory method, spectral measures and a lifting theorem. As a result, a Fredholm symbol calculus for the C*-algebra B or, equivalently, a faithful representation of the quotient C*-algebra B/K on a suitable Hilbert space is constructed and a Fredholm criterion for the operators B is an element of B is established. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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