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
Full-text PDF Free Access
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.
- 1. Ernst Albrecht and Florian-Horia Vasilescu, Semi-Fredholm complexes, Dilation theory, Toeplitz operators, and other topics (Timişoara/Herculane, 1982) Oper. Theory Adv. Appl., vol. 11, Birkhäuser, Basel, 1983, pp. 15–39. MR 789629
- 2. Ernst Albrecht and Florian-Horia Vasilescu, Stability of the index of a semi-Fredholm complex of Banach spaces, J. Funct. Anal. 66 (1986), no. 2, 141–172. MR 832988, https://doi.org/10.1016/0022-1236(86)90070-4
- 3. C.-G. Ambrozie, Stability of the index of a Fredholm symmetrical pair, J. Operator Theory 25 (1991), no. 1, 61–77. MR 1191254
- 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. Raul E. Curto, Fredholm and invertible 𝑛-tuples of operators. The deformation problem, Trans. Amer. Math. Soc. 266 (1981), no. 1, 129–159. MR 613789, https://doi.org/10.1090/S0002-9947-1981-0613789-6
- 8. J. Eschmeier, Analytic spectral mapping theorems for joint spectra, Operator Theory: Advances and Applications 24 (1987), 167-181.
- 9. A. S. Faĭnšteĭn, Stability of Fredholm complexes of Banach spaces with respect to perturbations which are small in 𝑞-norm, Izv. Akad. Nauk Azerbaĭdzhan. SSR Ser. Fiz.-Tekhn. Mat. Nauk 1 (1980), no. 1, 3–8 (Russian, with English and Azerbaijani summaries). MR 596125
- 10. A. S. Faĭnshteĭn and V. S. Shul′man, Stability, under perturbations that are small with respect to the measure of noncompactness, of the index of a short Fredholm complex of Banach spaces, Spectral theory of operators, No. 4, “Èlm”, Baku, 1982, pp. 189–198 (Russian). MR 800296
- 11. Constantin Niculescu and Nicolae Popa, Elemente de teoria spaţiilor Banach, Editura Academiei Republicii Socialiste România, Bucharest, 1981 (Romanian). With an English summary. MR 616450
- 12. Mihai Putinar, Some invariants for semi-Fredholm systems of essentially commuting operators, J. Operator Theory 8 (1982), no. 1, 65–90. MR 670178
- 13. Mihai Putinar, Base change and the Fredholm index, Integral Equations Operator Theory 8 (1985), no. 5, 674–692. MR 813356, https://doi.org/10.1007/BF01201709
- 14. Joseph L. Taylor, A joint spectrum for several commuting operators, J. Functional Analysis 6 (1970), 172–191. MR 0268706, https://doi.org/10.1016/0022-1236(70)90055-8
- 15. F.-H. Vasilescu, Stability of the index of a complex of Banach spaces, J. Operator Theory 2 (1979), no. 2, 247–275. MR 559608
- 16. F.-H. Vasilescu, The stability of the Euler characteristic for Hilbert complexes, Math. Ann. 248 (1980), no. 2, 109–116. MR 573342, https://doi.org/10.1007/BF01421951
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:
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