A perturbation result for \(q\)-open quotient morphisms in normed spaces and applications to linear relations. (English) Zbl 1179.47010
Using a result of E.Albrecht and F.-H.Vasilescu [see Theorem 3 in J. Funct.Anal.66, 141–172 (1986; Zbl 0592.47008)], the author studies the behaviour of the topological index of a quotient morphism between normed spaces under small perturbations. As an application, a necessary and sufficient conditions for the stability of the topological index of an open linear relation (multivalued operator) with closed multivalued part between normed spaces under small perturbations with linear relations is obtained.
Reviewer: Mohamed Zohry (Tétouan)
Citations:
Zbl 0592.47008References:
| [1] | Albrecht, E.; Vasilescu, F.-H., Semi-Fredholm complexes, Oper. Theory Adv. Appl., 11, 15-39 (1983) · Zbl 0527.47008 |
| [2] | Albrecht, E.; Vasilescu, F.-H., Stability of the index of a semi-Fredholm complex of Banach spaces, J. Funct. Anal., 66, 141-172 (1986) · Zbl 0592.47008 |
| [3] | Alvarez, T., On almost semi-Fredholm linear relations in normed spaces, Glasg. Math. J., 47, 187-193 (2005) · Zbl 1090.47001 |
| [4] | Alvarez, T.; Cross, R. W.; Wilcox, D., Multivalued Fredholm type operators with abstract generalised inverses, J. Math. Anal. Appl., 261, 403-417 (2001) · Zbl 0993.47012 |
| [5] | Alvarez, T.; Wilcox, D., Perturbation theory of multivalued Atkinson operators in normed spaces, Bull. Austral. Math. Soc., 76, 195-204 (2007) · Zbl 1145.47001 |
| [6] | Ambrozie, C.-G.; Muller, V., Duality in quotient Banach spaces, Rev. Roumaine Math. Pures Appl., 45, 555-563 (2000) · Zbl 0994.47001 |
| [7] | Ambrozie, C.-G.; Vasilescu, F.-H., Banach Space Complexes, Math. Appl., vol. 334 (1995), Kluwer Academic Publishers Group: Kluwer Academic Publishers Group Dordrecht · Zbl 0837.47009 |
| [8] | Arens, R., Operational calculus of linear relations, Pacific J. Math., 11, 9-23 (1961) · Zbl 0102.10201 |
| [9] | Coddington, E. A., Multivalued operators and boundary value problems, (Lecture Notes in Math., vol. 183 (1971), Springer: Springer Berlin), 2-8 · Zbl 0219.47042 |
| [10] | Cross, R. W., Multivalued Linear Operators (1998), Marcel Dekker: Marcel Dekker New York · Zbl 0940.15002 |
| [11] | Favini, A.; Yagi, A., Multivalued linear operators and dengenerate evolution equations, Ann. Mat. Pura Appl., 163, 353-384 (1993) · Zbl 0786.47037 |
| [12] | D. Gheorghe, A Kato perturbation-type result for open linear relations in normed spaces, Bull. Austral. Math. Soc., in press; D. Gheorghe, A Kato perturbation-type result for open linear relations in normed spaces, Bull. Austral. Math. Soc., in press · Zbl 1166.47005 |
| [13] | Harte, R., Invertibility and Singularity for Bounded Linear Operators (1988), Marcel Dekker: Marcel Dekker New York · Zbl 0636.47001 |
| [14] | Kato, T., Perturbation Theory for Linear Operators (1966), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York · Zbl 0148.12601 |
| [15] | Vasilescu, F.-H., Spectral theory in quotient Fréchet spaces. I, Rev. Roumaine Math. Pures Appl., 32, 561-579 (1987) · Zbl 0665.46058 |
| [16] | Vasilescu, F.-H., Spectral theory in quotient Fréchet spaces. II, J. Operator Theory, 21, 145-202 (1989) · Zbl 0782.46005 |
| [17] | Waelbroeck, L., Bornological Quotients, Classe des sciences (2005), Académie Royale de la Belgique · Zbl 1084.46001 |
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