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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
DOI: https://doi.org/10.1090/S0002-9939-99-05532-X
Published electronically: November 23, 1999
MathSciNet review: 1694871
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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.


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  • 1. Jacques Dixmier, Les 𝐶*-algèbres et leurs représentations, Deuxième édition. Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars Éditeur, Paris, 1969 (French). MR 0246136
  • 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
  • 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, https://doi.org/10.1007/BF02392873
  • 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
  • 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, https://doi.org/10.1016/0001-8708(92)90059-T
  • 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
    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
  • 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
  • 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
  • 15. B. A. Plamenevskij and V. N. Senichkin. Pseudodifferential operators on manifolds with singularities. Preprint, in Russian, 1997.

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Additional Information

Robert Lauter
Affiliation: Fachbereich 17 - Mathematik, Universität Mainz, D-55099 Mainz, Germany
Email: lauter@mathematik.uni-mainz.de

DOI: https://doi.org/10.1090/S0002-9939-99-05532-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