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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$K$-theory of $\mathrm{SG}$-pseudo-differential algebras


Author: Fabio Nicola
Journal: Proc. Amer. Math. Soc. 131 (2003), 2841-2848
MSC (2000): Primary 46L80; Secondary 58J40, 19K56
Published electronically: January 8, 2003
MathSciNet review: 1974341
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Abstract | References | Similar Articles | Additional Information

Abstract: We are concerned with the so-called ${\rm SG}$-pseudo-differential calculus. We describe the spectrum of the unital and commutative $C^\ast$-algebra given by the norm closure of the space of $0$-order pseudo-differential operators modulo compact operators; other related algebras are also considered. Finally, their $K$-theory is computed.


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  • 1. Atiyah M.F., $K$-theory, W.A. Benjamin, New York, 1967. MR 36:7130
  • 2. Blackadar B., $K$-theory for operator algebras, Springer, New York, 1998. MR 99g:46104
  • 3. Cordes H.O., A global parametrix for pseudo-differential operators over $\mathbb{R}^n$, with applications, Reprint, SFB 72, Universität Bonn, 1976.
  • 4. Cordes H.O., The technique of pseudodifferential operators, Cambridge University Press, 1995. MR 96b:35001
  • 5. Coriasco S., Fourier integral operators in SG classes. II. Application to SG hyperbolic Cauchy problems, Ann. Univ. Ferrara, 44 (1998), 81-122. MR 2001m:47106
  • 6. Feygin V.I., Two algebras of pseudodifferential operators in $\mathbb{R}^n$ and some applications, Trudy Moskov. Mat. Obshch., 36 (1977), 155-194.
  • 7. Grushin V.V., Pseudodifferential operators in $\mathbb{R}^n$ with bounded symbols, Funkc. Anal., 3 (1970), 37-50.
  • 8. Hörmander L., The analysis of linear partial differential operators III, Springer-Verlag, Berlin, 1985. MR 87d:35002a; corrected reprint MR 95h:35255
  • 9. Lauter R., Monthubert B., Nistor V., Pseudodifferential analysis on continuous family groupoids, Doc. Math., 5 (2000), 625-655 (electronic). MR 2002f:58046
  • 10. Lauter R., Moroianu S., Fredholm theory for degenerate pseudodifferential operators on manifolds with fibred boundaries, Commun. P.D.E., 26 (2001), 233-283. MR 2002e:58052
  • 11. Melo S.T., Nest R., Schrohe E., $C^\ast$-structure and K-Theory of Boutet de Monvel's algebra, preprint November 2001, Potsdam.
  • 12. Melrose R.B., Spectral and Scattering theory of the Laplacian on asymptotically Euclidean spaces, in Spectral and Scattering theory, M. Ikawa, ed. Marcel Dekker, 1994, 85-130. MR 95k:58168
  • 13. Melrose R.B., Geometric scattering theory, Cambridge University Press, 1995. MR 96k:35129
  • 14. Melrose R.B., Zworski M., Scattering metric and geodesic flow at infinity, Invent. Math., 124 (1996), 389-436. MR 96k:58230
  • 15. Melrose R.B., Nistor V., $K$-theory of $C^\ast$-algebras of $b$-pseudodifferential operators, Geom. Funct. Anal., 8 (1998), 88-122. MR 99i:58145
  • 16. Parenti C., Operatori pseudo-differentiali in $\mathbb{R}^n$ e applicazioni, Annali Mat. Pura Appl., 93 (1972), 359-389. MR 55:10838
  • 17. Schrohe E., Spaces of weighted symbols and weighted Sobolev spaces on manifolds, vol. 1256 LNM, 360-377, Springer-Verlag, Berlin-Heidelberg, 1987. MR 89g:58200
  • 18. Schulze B.-W., Boundary Value Problems and Singular Pseudo-differential Operators, J. Wiley & Sons, Chichester, New York, 1998. MR 99m:35281
  • 19. Shubin M.A., Pseudodifferential operators in $\mathbb{R}^n$, Dokl. Akad. Nauk SSSR, 196 (1971), 316-319.
  • 20. Shubin M.A., Pseudodifferential operators and spectral theory, Springer-Verlag, Berlin, $1987$. MR 88c:47105
  • 21. Wegge-Olsen N.E., $K$-theory and $C^\ast$-algebras, Oxford University Press, New York, 1993. MR 95c:46116

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Additional Information

Fabio Nicola
Affiliation: Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy
Email: nicola@dm.unito.it

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06837-0
PII: S 0002-9939(03)06837-0
Keywords: $K$-theory, $C^\ast$-algebras, pseudo-differential operators
Received by editor(s): January 23, 2002
Received by editor(s) in revised form: April 7, 2002
Published electronically: January 8, 2003
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2003 American Mathematical Society