Hostname: page-component-f554764f5-nqxm9 Total loading time: 0 Render date: 2025-04-11T15:15:03.817Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear relations on hereditarily indecomposable normed spaces

Published online by Cambridge University Press:  17 April 2009

Teresa Álvarez
Teresa Álvarez
Affiliation:
Department of Mathematics, University of Oviedo, 33007, Oviedo, Asturias, Spain e-mail: [email protected]
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.

We introduce the notion of hereditarily indecomposable normed space and we prove that this class of normed spaces may be characterised by means of F+ and strictly singular linear relations. We also show that if X is a complex hereditarily indecomposable normed space then every partially continuous linear relation in X with dense domain can be written as λI + S, where λ ∈ ℂ and S is a strictly singular linear relation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 2 , October 2006 , pp. 289 - 300
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Agarwal, R.P., Meehan, M. and O'Regan, D., Fixed point theory and applications (Cambridge University Press, Cambridge, 2001).Google Scholar
[2]Álvarez, T., Cross, R.W. and Wilcox, D., ‘Quantities related to upper and lower semiFredholm type linear relations’, Bull. Austr. Math. Soc. 66 (2002), 275–289.CrossRefGoogle Scholar
[3]Álvarez, T., ‘On almost semiFredholm linear relations in normed spaces’, Glasgow Math. J. 47 (2005), 187–193.CrossRefGoogle Scholar
[4]Cross, R.W., Multivalued linear operators (Marcel Dekker, New York, 1998).Google Scholar
[5]Edmunds, D.E. and Evans, W.D., Spectral theory and differential operators (Clarendon, Oxford, Oxford, 1987).Google Scholar
[6]Favini, A. and Yagi, A., ‘Multivalued linear operators and degenerate evolution equations’, Ann. Mat. Pura. Appl. (4) 163 (1993), 353–384.CrossRefGoogle Scholar
[7]Goldberg, S., Unbounded linear operators. Theory and applications (McGraw-Hill, New York, 1966).Google Scholar
[8]Gorniewicz, L., Topological fixed point theory of multivalued mappings (Kluwer, Dordrecht, 1999).CrossRefGoogle Scholar
[9]Gowers, W.T. and Maurey, B., ‘The unconditional basic sequence problem’, J. Amer. Math. Soc. 6 (1993), 851–874.Google Scholar
[10]Gromov, M., Partial differential relations (Springer–Verlag, Berlin, 1986).Google Scholar
[11]Heuser, H.G., Functional analysis (Wiley, Chichester, 1982).Google Scholar
[12]Muresan, M., ‘On a boundary value problem for quasi-linear differential inclusions of evolution’, Collect. Math. 45 (1994), 165–175.Google Scholar
[13]Von Neumann, J., Functional operators II. The Geometry of orthogonal Spaces, Annals of Math. Studies 22 (Princeton University Press, Princeton N.J., 1950).Google Scholar
[14]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
[15]Weiss, L., ‘Perturbation classes of semi-Fredholm operators’, Math. Z. 178 (1981), 429–442.CrossRefGoogle Scholar