Abstract
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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C.A.Berger, L.A.Coburn, Wiener-Hopf operators on U2 Int. Equat. Oper. Theory 2 (1979) 139–173
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
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
N. Bourbaki, Groupes et algèbres de Lie, Chapitres 2 et 3 Hermanm, Paris, 1972
L.Boutet de Monvel, On the index of Toeplitz operators of several complex variables, Invent. Math. 50 (1979) 249–272
M.Breuer, Fredholm theories in von Neumann algebras I, II Math. Ann. 178 (1968) 243–254 Math. Ann. 180 (1969) 313–325
M.Breuer, Theory of Fredholm operators and vector bundles relative to a von Neumann algebra Rocky Mount. J. Math. 3 (1973) 383–429
R.G.Douglas, Banach algebra techniques in the theory of Toeplitz operators, Regional Conf. in Math. 15, Providence, Rhode Island, 1973
M.Karoubi, K-theory, Springer, Berlin-Heidelberg-New York, 1978
R.Palais, Homotopy type of infinite dimensional manifolds Topology 5 (1966) 1–16
E. Spanier, Algebraic topology, McGraw Hill, New York, 1966
M.Takesaki, Theory of Operator Algebras I, Springer, Berlin-Heidelberg-New York, 1979
J.Tomiyama, K.Yabuta, Toeplitz operators for uniform algebras, Tôhoku Math. J. 30 (1978) 117–129
U.Venugopalkrishna, Fredholm operators associated with strongly pseudoconvex domains in ℂn. J. Funct. Anal. 9 (1972) 349–373
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
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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