The ghost of an index theorem

Harte, Robin

doi:10.1090/S0002-9939-1989-0975646-8

The ghost of an index theorem
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Proc. Amer. Math. Soc. 106 (1989), 1031-1033 Request permission

Correction: Proc. Amer. Math. Soc. 128 (2000), 3145-3148.

Abstract:

The "index theorem" whose spirit we invoke says that the index of a product of Fredholm operators is the sum of their indexes; our extension is to operators with "generalized inverses".

References

S. R. Caradus, Generalized inverses and operator theory, Queen’s Papers in Pure and Applied Mathematics, vol. 50, Queen’s University, Kingston, Ont., 1978. MR 523736
S. R. Caradus, W. E. Pfaffenberger, and Bertram Yood, Calkin algebras and algebras of operators on Banach spaces, Lecture Notes in Pure and Applied Mathematics, Vol. 9, Marcel Dekker, Inc., New York, 1974. MR 0415345
Robin Harte, Fredholm, Weyl and Browder theory, Proc. Roy. Irish Acad. Sect. A 85 (1985), no. 2, 151–176. MR 845539
Robin Harte, Invertibility and singularity for bounded linear operators, Monographs and Textbooks in Pure and Applied Mathematics, vol. 109, Marcel Dekker, Inc., New York, 1988. MR 920812
Harro G. Heuser, Functional analysis, A Wiley-Interscience Publication, John Wiley & Sons, Ltd., Chichester, 1982. Translated from the German by John Horváth. MR 640429
Mihai Putinar, Some invariants for semi-Fredholm systems of essentially commuting operators, J. Operator Theory 8 (1982), no. 1, 65–90. MR 670178
Angus Ellis Taylor and David C. Lay, Introduction to functional analysis, 2nd ed., John Wiley & Sons, New York-Chichester-Brisbane, 1980. MR 564653
Kung Wei Yang, Index of Fredholm operators, Proc. Amer. Math. Soc. 41 (1973), 329–330. MR 318946, DOI 10.1090/S0002-9939-1973-0318946-5
Donald Sarason, The multiplication theorem for Fredholm operators, Amer. Math. Monthly 94 (1987), no. 1, 68–70. MR 873608, DOI 10.2307/2323506