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

DOI:
https://doi.org/10.1090/S0002-9939-96-03283-2

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.

**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(2) (1986), 141-172. MR**66****87g:58011****3.**C.-G. Ambrozie,*Stability of the index of a Fredholm symmetrical pair*, J. Operator Theory(1991), 61-67. MR**25****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 -tuples of operators. The deformation problem*, Trans. Amer. Math. Soc.(1) (1981), 129-159. MR**266****82g:47010****8.**J. Eschmeier,*Analytic spectral mapping theorems for joint spectra*, Operator Theory: Advances and Applications(1987), 167-181.**24****9.**A. S. Fainshtein,*Stability of Fredholm complexes of Banach spaces with respect to perturbations which are small in -norm (Russian)*, Izvestya Akad. Nauk. Azer. S.S.R.(1980), 3-8. MR**1****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(1982), 189-198. MR**4****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(1982), 65-90. MR**8****84b:58009****13.**M. Putinar,*Base change and the Fredholm index*, Integral Equations Operator Theory(1985), 674-692. MR**8****87j:47020****14.**J. L. Taylor,*A joint spectrum for several commuting operators*, J. Functional Analysis(1970), 172-191. MR**6****42:3603****15.**F.-H. Vasilescu,*Stability of the index of a complex of Banach spaces*, J. Operator Theory(1979), 247-275. MR**2****83b:47025****16.**F.-H. Vasilescu,*The Stability of the Euler Characteristic for Hilbert Complexes*, Math. Ann.(1980), 109-116. MR**248****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

Email:
cambroz@imar.ro

DOI:
https://doi.org/10.1090/S0002-9939-96-03283-2

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