Abstract
Representations on Hilbert spaces for a nonlocal C*-algebra of singular integral operators with piecewise slowly oscillating coefficients and unitary shift operators are constructed. The group of unitary shift operators U g of the C*-algebra is associated with an amenable discrete group of homeomorphisms g:TT that have piecewise continuous derivatives and the same nonempty set of periodic points. An isometric C*-algebra homomorphism of the quotient C*-algebra , where is the ideal of compact operators, into an n× n matrix algebra associated to a C*-algebra of singular integral operators with shifts having only fixed points is established making use of a spectral measure. Based on this generalization of the Litvinchuk–Gohberg–Krupnik reduction scheme, a symbol calculus for the C*-algebra as well as a Fredholm criterion for the operators in are obtained.
Original language | Unknown |
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Pages (from-to) | 509-534 |
Journal | Integral Equations And Operator Theory |
Volume | 71 |
Issue number | 4 |
Publication status | Published - 1 Jan 2011 |