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- W2080342874 abstract "Let A denote the C*algebra of bounded operators on L2(R) generated by: (i) all multiplications a(M) by functions ain C[-infty,+infty], (ii) all multiplications by 2pi-periodic continuous functions and (iii) all Fourier multipliers F^{-1}b(M)F, where F denotes the Fourier transform and b is in C[-infty,+infty]. The Fredholm property for operators in A is governed by two symbols, the principal symbol sigma and an operator-valued symbol gamma. We give two proofs of the fact that K0(A) and K1(A) are isomorphic, respectively, to Z and Zoplus Z: by computing the connecting mappings in the standard K-theory six-term exact sequences associated to sigma and to gamma. For the second computation, we prove that the image of gamma is isomorphic to the direct sum of two copies of the crossed product of C[-infty,+infty] by an automorphism, and then use the Pimsner-Voiculescu exact sequence to compute its K-theory." @default.
- W2080342874 created "2016-06-24" @default.
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- W2080342874 date "2006-03-01" @default.
- W2080342874 modified "2023-09-24" @default.
- W2080342874 title "K-Theory of pseudodifferential operators with semi-periodic symbols" @default.
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- W2080342874 doi "https://doi.org/10.1007/s10977-006-0018-z" @default.
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