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The Euler characteristic is stable under compact perturbations

Author: Calin-Grigore Ambrozie
Journal: Proc. Amer. Math. Soc. 124 (1996), 2041-2050
MSC (1991): Primary 47A53; Secondary 47A55
MathSciNet review: 1322909
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Abstract: We prove in the general case the stability under compact perturbations of the index (i.e. the Euler characteristic) of a Fredholm complex of Banach spaces. In particular, we obtain the corresponding stability property for Fredholm multioperators. These results are the consequence of a similar statement, concerning more general objects called Fredholm pairs.

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  • 1. E. Albrecht and F.-H. Vasilescu, Semi-Fredholm complexes, Operator Theory: Advances and Applications, vol. 11, Birkhäuser-Verlag, Basel, 1983, pp. 15--39. MR 86i:47001
  • 2. E. Albrecht; F.-H. Vasilescu, Stability of the index of a semi-Fredholm complex of Banach spaces, J. Functional Analysis 66 (2) (1986), 141-172. MR 87g:58011
  • 3. C.-G. Ambrozie, Stability of the index of a Fredholm symmetrical pair, J. Operator Theory 25 (1991), 61-67. MR 94c:47012
  • 4. C.-G. Ambrozie, On Fredholm index in Banach spaces, preprint IMAR 6/'91.
  • 5. C.-G. Ambrozie, The solution of a problem on Fredholm complexes, preprint IMAR 30/'94.
  • 6. R. E. Curto, Fredholm and invertible tuples of bounded linear operators, Dissertation, State Univ. of New York at Stony Brook, 1978.
  • 7. R. E. Curto, Fredholm and invertible $n$-tuples of operators. The deformation problem, Trans. Amer. Math. Soc. 266 (1) (1981), 129-159. MR 82g:47010
  • 8. J. Eschmeier, Analytic spectral mapping theorems for joint spectra, Operator Theory: Advances and Applications 24 (1987), 167-181.
  • 9. A. S. Fainshtein, Stability of Fredholm complexes of Banach spaces with respect to perturbations which are small in $q$-norm (Russian), Izvestya Akad. Nauk. Azer. S.S.R. 1 (1980), 3-8. MR 82f:58009
  • 10. A. S. Fainshtein and V. S. Shul'man, Stability of the index of a short Fredholm complex of Banach spaces under perturbations that are small in the non-compactness measure (Russian), Spectral'naia teoria operatorov 4 (1982), 189-198. MR 86j:47014
  • 11. C. Niculescu; N. Popa, Elements of the Banach spaces theory (Romanian), The Acad. Publishing House, Bucharest, 1981. MR 82m:46010
  • 12. M. Putinar, Some invariants for semi-Fredholm systems of essentially commuting operators, J. Operator Theory 8 (1982), 65-90. MR 84b:58009
  • 13. M. Putinar, Base change and the Fredholm index, Integral Equations Operator Theory 8 (1985), 674-692. MR 87j:47020
  • 14. J. L. Taylor, A joint spectrum for several commuting operators, J. Functional Analysis 6 (1970), 172-191. MR 42:3603
  • 15. F.-H. Vasilescu, Stability of the index of a complex of Banach spaces, J. Operator Theory 2 (1979), 247-275. MR 83b:47025
  • 16. F.-H. Vasilescu, The Stability of the Euler Characteristic for Hilbert Complexes, Math. Ann. 248 (1980), 109-116. MR 82c:32022

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Additional Information

Calin-Grigore Ambrozie
Affiliation: Institute of Mathematics, Romanian Academy, P.O.Box 1-764 RO-70700 Bucharest, Romania

Keywords: Index, Fredholm complex of Banach spaces
Received by editor(s): December 21, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society