Hostname: page-component-cb9f654ff-nr592 Total loading time: 0 Render date: 2025-08-17T03:04:15.515Z Has data issue: false hasContentIssue false
  • English
  • Français

Homogeneous operators and essential complexes

Published online by Cambridge University Press:  18 May 2009

F.-H. Vasilescu
F.-H. Vasilescu
Affiliation:
Department of Mathematics, National Institute for Scientific And Technical Creation, Bdul Păaii 220, 77538 Bucharest, Rumania
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The aim of this work is to present a new approach to the concept of essential Fredholm complex of Banach spaces ([10], [2]; see also [11], [4], [6], [7] etc. for further connections), by using non-linear homogeneous mappings. We obtain some generalized homotopic properties of the class of essential Fredholm complexes, in our sense, which are then applied to establish its relationship with similar concepts. We also prove the stability of this class under small perturbations with respect to the gap topology.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 1 , January 1989 , pp. 73 - 85
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

1.Albrecht, E. and Vasilescu, F.-H., Semi-Fredholm complexes, pp. 15–39 in Operator Theory: Advances and Applications Vol. 11 (Birkhäuser-Verlag, Basel, 1983).Google Scholar
2.Albrecht, E. and Vasilescu, F.-H., Stability of the index of a semi-Fredholm complex of Banach spaces, J. Functional Analysis, 66 (1986), 141–172.CrossRefGoogle Scholar
3.Buoni, J. J., Harte, R., and Wickstead, T., Upper and lower Fredholm spectra, Proc. Amer. Math. Soc. 66 (1977), 309–314.Google Scholar
4.Curto, R. E., Fredholm and invertible tuples of operators. The deformation problem, Trans. Amer. Math. Soc. 266 (1981), 129–159.Google Scholar
5.Eschmeier, J., Analytic spectral mapping theorems for joint spectra, pp. 167–181 in Operator Theory: Advances and Applications Vol. 24 (Birkhäuser-Verlag, Basel, 1987).Google Scholar
6.Fainshtein, A. S., Stability of Fredholm complexes of Banach spaces with respect to perturbations which are small in q-norm (in Russian), Izv. Akad. Nauk Azerb. SSR 1 (1980), 3–7.Google Scholar
7.Fainshtein, A. S. and Shul'man, V. S., On Fredholm complexes of Banach spaces (in Russian), Functs. analiz prilozh. 14 (1980), 87–88.Google Scholar
8.Fainshtein, A. S. and Shul'man, V. S., Stability of the index of a short Fredholm complex of Banach spaces with respect to perturbations of small non-compactness measure (in Russian), Spectral'nay a teoriya operatorov, 4 (The Publishing House “Elm”, Baku, 1982).Google Scholar
9.Kato, T.. Perturbation theory for linear operators (Springer-Verlag, New York, 1966).Google Scholar
10.Putinar, M., Some invariants for semi-Fredholm systems of essentially commuting operators, J. Operator Theory 8 (1982), 65–90.Google Scholar
11.Segal, G., Fredholm complexes, Quart. J. Math. Oxford (2) 21 (1970), 385–402.CrossRefGoogle Scholar
12.Singer, I., Sur l'approximation uniforme des opérateurs linéaires compacts par des operateurs non linéaires de rang fini, Archiv der Math. 11 (1960), 289–293.CrossRefGoogle Scholar
13.Singer, I., Some classes of non-linear operators generalizing the metric projections onto Chebyshev subspaces, in Theory of Nonlinear Operators (Akademie-Verlag, Berlin, 1978).Google Scholar
14.Vasilescu, F.-H., Stability of the index of a complex of Banach spaces, J. Operator Theory 2 (1979), 247–275.Google Scholar
15.Vasilecsu, F.-H., Nonlinear objects in the linear analysis, pp. 265–278 in Operator Theory: Advances and Applications Vol. 14, (Birkhauser-Verlag, Basel, 1984).Google Scholar
16.Zaidenberg, M. G., Kreĭn, S. G., Kuchment, P. A. and Pankov, A. A., Banach bundles and linear operators, Russian Math. Surveys 30 (1975), 115–175.CrossRefGoogle Scholar