Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

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


The length of $C^{*}$-algebras
of $\mathbf{\mathrm{b}}$-pseudodifferential operators

Author: Robert Lauter
Journal: Proc. Amer. Math. Soc. 128 (2000), 1955-1961
MSC (2000): Primary 46L85, 58G40; Secondary 35S35, 46L80
Published electronically: November 23, 1999
MathSciNet review: 1694871
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We compute the length of the $C^{*}$-algebra generated by the algebra of b-pseudodifferential operators of order $0$ on compact manifolds with corners.

References [Enhancements On Off] (What's this?)

  • 1. Jacques Dixmier, Les 𝐶*-algèbres et leurs représentations, Deuxième édition. Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars Éditeur, Paris, 1969 (French). MR 0246136 (39 #7442)
  • 2. Alexander Dynin, Inversion problem for singular integral operators: 𝐶*-approach, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), no. 10, 4668–4670. MR 507929 (80c:46066)
  • 3. B. Gramsch. Some homogeneous spaces in the operator theory and $\Psi$-algebras. In Tagungsbericht Oberwolfach 42/81 - Funktionalanalysis: $C^{*}$-Algebren, 1981.
  • 4. R. Lauter. On the existence and structure of $\Psi^{*}$-algebras of totally characteristic operators on compact manifolds with boundary. Preprint Nr. 12/97, Fachbereich Mathematik, Johannes Gutenberg-Universität Mainz, October 1997. To appear in J. Funct. Anal.
  • 5. R. Lauter. O predstavleniyah $\Psi^{*}$- i $C^*$- algebr psevdodifferentsial'nyh operatorov na mnogoobraziyah s vershinami. In N. N. Ural'tseva, editor, Nelineinye uravneniya s chastnymi proizvodnymi i teoriya funktsii, volume 18 of Problemy matematicheskogo analiza, pages 85-117. Sankt-Peterburgskii universitet, November 1998. in Russian.
  • 6. P. A. Loya. On the b-pseudodifferential calculus on manifolds with corners. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, 1998.
  • 7. R. B. Melrose. Analysis on manifolds with corners. in preparation.
  • 8. Richard B. Melrose, Transformation of boundary problems, Acta Math. 147 (1981), no. 3-4, 149–236. MR 639039 (83f:58073),
  • 9. Richard B. Melrose, The Atiyah-Patodi-Singer index theorem, Research Notes in Mathematics, vol. 4, A K Peters, Ltd., Wellesley, MA, 1993. MR 1348401 (96g:58180)
  • 10. R. B. Melrose and V. Nistor. K-theory of $C^{*}$-algebras of b-pseudodifferential operators. Geometric and Functional Analysis, 8:88-122, 1998. CMP 98:07
  • 11. Richard B. Melrose and Paolo Piazza, Analytic 𝐾-theory on manifolds with corners, Adv. Math. 92 (1992), no. 1, 1–26. MR 1153932 (93h:58149),
  • 12. B. A. Plamenevskiĭ and V. N. Senichkin, Representations of 𝐶*-algebras generated by pseudodifferential operators in weighted spaces, Wave propagation. Scattering theory (Russian), Probl. Mat. Fiz., vol. 12, Leningrad. Univ., Leningrad, 1987, pp. 165–189, 259 (Russian). MR 923977 (89e:47074)
    M. Sh. Birman, M. Sh. Birman, and M. Sh. Birman (eds.), Wave propagation. Scattering theory, American Mathematical Society Translations, Series 2, vol. 157, American Mathematical Society, Providence, RI, 1993. A translation by Peter Zhevandrov of Wave propagation. Scattering theory (Russian), Leningrad.\ Univ., Leningrad, 1987 [ MR0923966 (88j:00016)]; Translation edited by Simeon Ivanov. MR 1252219 (94g:00020)
  • 13. B. A. Plamenevskiĭ and V. N. Senichkin, Solvable operator algebras, Algebra i Analiz 6 (1994), no. 5, 1–87 (Russian); English transl., St. Petersburg Math. J. 6 (1995), no. 5, 895–968. MR 1318302 (95k:47038)
  • 14. B. A. Plamenevskij and V. N. Senichkin, On composition series in algebras of pseudodifferential operators and in algebras of Wiener-Hopf operators, Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras, Math. Top., vol. 11, Akademie Verlag, Berlin, 1996, pp. 373–404. MR 1409838 (97h:47050)
  • 15. B. A. Plamenevskij and V. N. Senichkin. Pseudodifferential operators on manifolds with singularities. Preprint, in Russian, 1997.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L85, 58G40, 35S35, 46L80

Retrieve articles in all journals with MSC (2000): 46L85, 58G40, 35S35, 46L80

Additional Information

Robert Lauter
Affiliation: Fachbereich 17 - Mathematik, Universität Mainz, D-55099 Mainz, Germany

PII: S 0002-9939(99)05532-X
Keywords: Length of solvable $C^{*}$-algebras, b-pseudodifferential operators, manifolds with corners
Received by editor(s): June 23, 1998
Received by editor(s) in revised form: August 12, 1998
Published electronically: November 23, 1999
Additional Notes: This work was supported by a scholarship of the German Academic Exchange Service (DAAD) within the Hochschulsonderprogramm III von Bund und Ländern.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia