Bulletin (New Series) of the American Mathematical Society

Contributions to the $K$-theory of $C^*$-algebras of Toeplitz and singular integral operators

Paul S. Muhly, Ian F. Putnam, and Jingbo Xia

Full-text: Open access

Article information

Bull. Amer. Math. Soc. (N.S.), Volume 21, Number 1 (1989), 47-50.

First available in Project Euclid: 4 July 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 47G05 46M20: Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx] 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]


Muhly, Paul S.; Putnam, Ian F.; Xia, Jingbo. Contributions to the $K$-theory of $C^*$-algebras of Toeplitz and singular integral operators. Bull. Amer. Math. Soc. (N.S.) 21 (1989), no. 1, 47--50. https://projecteuclid.org/euclid.bams/1183555122

Export citation


  • [CP] R. Carey and J. Pincus, Mosaics, principal functions, and mean motion in von Neumann algebras, Acta Math. 138 (1977), 153-218.
  • [CDSS] L. Coburn, R. G. Douglas, D. Schaeffer and I. Singer, On C*-algebras of operators on a half-space II, Index theory, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 69-79.
  • [Cl] A. Connes, Sur la théorie non commutative de l'intégration, Algèbres d'Opérateurs, Lecture Notes in Math., vol. 725, Springer-Verlag, Berlin and New York, 1979, pp. 19-143.
  • [C2] A. Connes, C*-algèbres et géométrie différentielle, C. R. Acad. Sci. Paris Sér. A 290 (1980), 599-604.
  • [C3] A. Connes, An analogue of the Thom isomorphism for crossed products of a C*-algebra by an action of R, Adv. in Math. 39 (1981), 31-55.
  • [CMX] R. Curto, P. Muhly and J. Xia, Toeplitz operators on flows, preprint.
  • [D1] R. G. Douglas, Elliptic invariants for differential operators, Proc. Sympos. on the Mathematical Heritage of Hermann Weyl, Proc. Sympos. Pure Math., vol. 48 Amer. Math. Soc., Providence, R.I., 1988, pp. 275-284.
  • [D2] R. G. Douglas, Another look at real-valued index theory, Surveys of Some Recent Results in Operator Theory, Vol. II, (J. B. Conway and B. B. Morrel eds.), Pitman Research Notes in Mathematics Series 192, New York, 1988, pp. 91-120.
  • [DHK1] R. G. Douglas, S. Hurder and J. Kaminker, Toeplitz operators and the eta invariant: the case of S1, preprint.
  • [DHK2] R. G. Douglas, S. Hurder and J. Kaminker, The longitudinal cyclic cocycle and the index of Toeplitz operators, preprint.
  • [FS] T. Fack and G. Skandalis, Connes's analogue of the Thom isomorphism for the Kasparov groups, Invent. Math. 64 (1981), 7-14.
  • [GF] I. Gohberg and I. Feldman, On Wiener-Hopf integral difference equations, Dokl. Akad. Nauk SSSR 183 (1968), 25-28=Soviet Math. Dokl. 9 (1968), 1312-1316.
  • [JK] R. Ji and J. Kaminker, The K-theory of Toeplitz extensions, J. Operator Theory 19 (1988), 347-354.
  • [JX] R. Ji and J. Xia, On the classification of commutator ideals, J. Funct. Anal. 78 (1988), 208-232.
  • [R] M. Rieffel, Connes' analogue for crossed products of the Thom isomorphism, Contemporary Math., vol. 10, Amer. Math. Soc. Providence, R.I., 1980, pp. 143-154.
  • [X] J. Xia, The K-theory and the invertibility of almost periodic Toeplitz operators, Integral Equations and Operator Theory 11 (1988), 267-286.