|
The Euler characteristic is stable under compact perturbations
Author(s):
Calin-Grigore
Ambrozie
Journal:
Proc. Amer. Math. Soc.
124
(1996),
2041-2050.
MSC (1991):
Primary 47A53;
Secondary 47A55
MathSciNet review:
1322909
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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.
References:
- 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
 -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
 -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
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
47A53,
47A55
Retrieve articles in all Journals with
MSC (1991):
47A53,
47A55
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:
10.1090/S0002-9939-96-03283-2
PII:
S 0002-9939(96)03283-2
Keywords:
Index,
Fredholm complex of Banach spaces
Received by editor(s):
December 21, 1994
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1996,
American Mathematical Society
|
