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Some continuous index theorems

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In this paper we give criteria of Fredholmness and index theorems for Toeplitz operators whose symbols take values in a W*-algebra factor of type II1.

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References

  1. C.A.Berger, L.A.Coburn, Wiener-Hopf operators on U2 Int. Equat. Oper. Theory 2 (1979) 139–173

    Google Scholar 

  2. C.A.Berger, L.A.Coburn, A.Koranyi, Opérateurs de Wiener-Hopf sur les sphères de Lie, C. R. Acad. Sci. Paris Sér. A+B 290 (1980) A989–991

    Google Scholar 

  3. C.A.Berger, L.A.Coburn, A.Lebow, Representation and index theory for C*-algebras generated by commuting isometries J. Funct. Anal. 27 (1978) 51–99

    Google Scholar 

  4. N. Bourbaki, Groupes et algèbres de Lie, Chapitres 2 et 3 Hermanm, Paris, 1972

    Google Scholar 

  5. L.Boutet de Monvel, On the index of Toeplitz operators of several complex variables, Invent. Math. 50 (1979) 249–272

    Google Scholar 

  6. M.Breuer, Fredholm theories in von Neumann algebras I, II Math. Ann. 178 (1968) 243–254 Math. Ann. 180 (1969) 313–325

    Google Scholar 

  7. M.Breuer, Theory of Fredholm operators and vector bundles relative to a von Neumann algebra Rocky Mount. J. Math. 3 (1973) 383–429

    Google Scholar 

  8. R.G.Douglas, Banach algebra techniques in the theory of Toeplitz operators, Regional Conf. in Math. 15, Providence, Rhode Island, 1973

  9. M.Karoubi, K-theory, Springer, Berlin-Heidelberg-New York, 1978

    Google Scholar 

  10. R.Palais, Homotopy type of infinite dimensional manifolds Topology 5 (1966) 1–16

    Google Scholar 

  11. E. Spanier, Algebraic topology, McGraw Hill, New York, 1966

    Google Scholar 

  12. M.Takesaki, Theory of Operator Algebras I, Springer, Berlin-Heidelberg-New York, 1979

    Google Scholar 

  13. J.Tomiyama, K.Yabuta, Toeplitz operators for uniform algebras, Tôhoku Math. J. 30 (1978) 117–129

    Google Scholar 

  14. U.Venugopalkrishna, Fredholm operators associated with strongly pseudoconvex domains in ℂn. J. Funct. Anal. 9 (1972) 349–373

    Google Scholar 

  15. L.A.Coburn, R.G.Douglas, I.M.Singer, An index theorem for Wiener-Hopf operators on the discrete quarterplane, J. Differential Geom. 6 (1972) 587–592

    Google Scholar 

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Schröder, H. Some continuous index theorems. Integr equ oper theory 7, 868–883 (1984). https://doi.org/10.1007/BF01195870

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  • DOI: https://doi.org/10.1007/BF01195870

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