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STRICTLY SINGULAR PERTURBATION OF ALMOST SEMI-FREDHOLM LINEAR RELATIONS IN NORMED SPACES

Published online by Cambridge University Press:  13 August 2013

T. ÁLVAREZ
T. ÁLVAREZ*
Affiliation:
Department of Mathematics, University of Oviedo, C/Calvo Sotelo s/n, Oviedo 33007, Asturias, Spain e-mail: seco@uniovi.es
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Abstract

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In this paper, we introduce the notions of almost upper semi-Fredholm and strictly singular pairs of subspaces and show that the class of almost upper semi-Fredholm pairs of subspaces is stable under strictly singular pairs perturbation. We apply this perturbation result to investigate the stability of almost semi-Fredholm multi-valued linear operators in normed spaces under strictly singular perturbation as well as the behaviour of the index under perturbation.

Keywords

47A06
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 1 , January 2014 , pp. 211 - 219
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

REFERENCES

1.Agarwal, R. P., Meehan, M. and O'Regan, D., Fixed point theory and applications (Cambridge University Press, Cambridge, UK, 2001).CrossRefGoogle Scholar
2.Álvarez, T., On almost semi-Fredholm linear relations in normed spaces, Glasgow Math. J. 47 (2005), 187–193.Google Scholar
3.Álvarez, T., On the perturbation of semi-Fredholm relations with complemented ranges and null spaces, Acta Math. Sinica (English Series) 26 (2010), 1545–1554.Google Scholar
4.Álvarez, 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.Álvarez, T., Cross, R. W. and Wilcox, D., Quantities related to upper and lower semi-Fredholm-type linear relations, Bull. Austr. Math. Soc. 66 (2002), 275–289.Google Scholar
6.Coddington, E. A. and Dijksma, A., Self-adjoint subspaces and eigenfunction expansions for ordinary differential subspaces, J. Differ. Equations 20 (1976), 473–526.CrossRefGoogle Scholar
7.Cross, R. W., Multivalued linear operators (Marcel Dekker, New York, NY, 1998).Google Scholar
8.Dijksma, A., El Sabbah, A. and de Snoo, H. S. V., Self-adjoint extensions of regular canonical systems with Stieltjes boundary conditions, J. Math. Anal. Appl. 152 (1990), 546–583.CrossRefGoogle Scholar
9.Favini, A. and Yagi, A., Multivalued linear operators and degenerate evolution equations, Ann. Mat. Pura. Appl. 163 (1993), 353–384.Google Scholar
10.Gheorghe, D., Erratum ‘Stability of the index of a linear relation under compact perturbations’ (Studia Math. 180 (2007), 95–102), Studia Math. 189 (2) (2008), 201–204.CrossRefGoogle Scholar
11.Gheorghe, D., A Kato perturbation-type result for open linear relations in normed spaces, Bull. Austr. Math. Soc. 79 (2009), 85–101.Google Scholar
12.Goldberg, S., Unbounded linear operators. Theory and applications (Dover, New York, NY, 1966).Google Scholar
13.González, M., Fredholm theory for pairs of closed subspaces of a Banach space, J. Math. Anal. Appl. 305 (2005), 53–62.CrossRefGoogle Scholar
14.Gorniewicz, L., Topological fixed point theory of multivalued mappings (Kluwer, Dordrecht, Netherlands, 1999).Google Scholar
15.Gromov, M., Partial differential relations (Springer-Verlag, Berlin, Germany, 1986).Google Scholar
16.Kato, T., Perturbation theory for nullity, deficiency and other quantities of linear operators, J. d'Analyse Math. 6 (1958), 273–322.CrossRefGoogle Scholar
17.Labuschagne, L. E., The perturbation of relatively open operators with reduced index, Proc. Math. Cambridge 112 (1992), 385–402.Google Scholar
18.Muresan, M., On a boundary value problem for quasi-linear differential inclusions of evolution, Collect. Math. 45 (1994), 165–175.Google Scholar
19.von Neumann, J., Functional operators II. The geometry of orthogonal spaces, Annals of Mathematics Studies, 22 (Princeton University Press, Princeton, NJ, 1950).Google Scholar
20.Román-Flores, H., Flores-Franulic, A., Rojas-Medar, M. A. and Bassanezi, R. C., Stability of the fixed points set of fuzzy contractions, Appl. Math. Lett. 11 (1998), 33–37.CrossRefGoogle Scholar
21.Sandovici, A. and de Snoo, H., An index formula for the product of linear relations, Lin. Alg. Appl. 431 (2009), 2160–2171.Google Scholar