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A KATO PERTURBATION-TYPE RESULT FOR OPEN LINEAR RELATIONS IN NORMED SPACES

Part of: General theory of linear operators

Published online by Cambridge University Press:  10 March 2009

DANA GHEORGHE
DANA GHEORGHE*
Affiliation:
Department of Mathematics, University of Piteşti, 110040 Piteşti, Romania (email: gheorghedana@yahoo.com)
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Abstract

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Using some techniques of perturbation theory for Banach space complexes, we obtain necessary and sufficient conditions for the stability of the topological index of an open linear relation under small (with respect to the gap topology) perturbations with linear relations.

Keywords

linear relationstopological indexBanach space complexes

MSC classification

Secondary: 47A06: Linear relations (multivalued linear operators)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 1 , February 2009 , pp. 85 - 101
Copyright
Copyright © Australian Mathematical Society 2009

References

[1] Albrecht, E. and Vasilescu, F.-H., ‘Stability of the index of a semi-Fredholm complex of Banach spaces’, J. Funct. Anal. 66 (1986), 141–172.Google Scholar
[2] Alvarez, T., ‘On almost semi-Fredholm linear relations in normed spaces’, Glasgow Math. J. 47 (2005), 187–193.Google Scholar
[3] Alvarez, T., ‘Characterisations of open multivalued linear operators’, Studia Math. 175 (2006), 205–212.Google Scholar
[4] Alvarez, T., Cross, R. W. and Wilcox, D., ‘Multivalued Fredholm type operators with abstract generalised inverses’, J. Math. Anal. Appl. 261 (2001), 403–417.CrossRefGoogle Scholar
[5] Alvarez, T. and Wilcox, D., ‘Perturbation theory of multivalued Atkinson operators in normed spaces’, Bull. Austral. Math. Soc. 76 (2007), 195–204.Google Scholar
[6] Ambrozie, C.-G. and Vasilescu, F.-H., Banach Space Complexes, Mathematics and its Applications, 334 (Kluwer Academic, Dordrecht, 1995).Google Scholar
[7] Arens, R., ‘Operational calculus of linear relations’, Pacific J. Math. 11 (1961), 9–23.CrossRefGoogle Scholar
[8] Coddington, E. A., Multivalued Operators and Boundary Value Problems, Lecture Notes in Mathematics, 183 (Springer, Berlin, 1971), pp. 2–8.Google Scholar
[9] Cross, R. W., Multivalued Linear Operators (Marcel Dekker, New York, 1998).Google Scholar
[10] Favini, A. and Yagi, A., ‘Multivalued linear operator and dengenerate evolution equations’, Ann. Mat. Pura Appl. 163 (1993), 353–384.Google Scholar
[11] Harte, R., Invertibility and Singularity for Bounded Linear Operators (Marcel Dekker, New York, 1988).Google Scholar
[12] Kato, T., Perturbation Theory for Linear Operators (Springer, Berlin, 1966), pp. 233–304; Lecture Notes in Pure and Appl. Math., 83, Dekker, New York, 1983.Google Scholar
[13] Vasilescu, F.-H., ‘Spectral theory in quotient Frechét spaces. I’, Rev. Roumaine Math. Pures Appl. 32 (1987), 561–579.Google Scholar
[14] Vasilescu, F.-H., ‘Spectral theory in quotient Frechét spaces. II’, J. Operator Theory 21 (1989), 145–202.Google Scholar