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- W2952797377 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.
- W2952797377 created "2019-06-27" @default.
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- W2952797377 creator A5074799149 @default.
- W2952797377 date "2005-11-04" @default.
- W2952797377 modified "2023-09-27" @default.
- W2952797377 title "K-Theory of pseudodifferential operators with semi-periodic symbols" @default.
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