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Surjectivity of linear operators from a Banach space into itself

Published online by Cambridge University Press:  17 April 2009

Dimosthenis Drivaliaris  and
Nikos Yannakakis
Dimosthenis Drivaliaris
Affiliation:
Department of Financial and Management Engineering, University of the Aegean, 31, Fostini Str., 82100 Chios, Greece, e-mail: d.drivaliaris@fme.aegean.gr
Nikos Yannakakis
Affiliation:
Department of Mathematics, School of Applied Mathematics and Natural Sciences, National Technical University of Athens, Iroon Polytexneiou 9, 15780 Zografou, Greece, e-mail: nyian@math.ntua.gr
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We show that linear operators from a Banach space into itself which satisfy some relaxed strong accretivity conditions are invertible. Moreover, we characterise a particular class of such operators in the Hilbert space case. By doing so we manage to answer a problem posed by B. Ricceri, concerning a linear second order partial differential operator.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 1 , August 2007 , pp. 143 - 154
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Deimling, K., Nonlinear functional analysis (Springer-Verlag, Berlin, 1985).CrossRefGoogle Scholar
[2]Hu, S. and Papageorgiou, N. S., Handbook of multivalued analysis, Vol. I (Kluwer Academic Publishers, Dordrecht, 1997).CrossRefGoogle Scholar
[3]Ricceri, B., ‘Existence theorems for nonlinear problems’, Rend. Accad. Naz. Sci. XL Mem. Mat. (5) 11 (1987), 77–99.Google Scholar
[4]Ricceri, B., ‘On some motivated conjectures and problems’, Mathematiche (Catania) 51 (1996), 369–373.Google Scholar
[5]Raymond, J. Saint, ‘A generalization of Lax-Milgram's theorem’, Matematiche (Catania) 52 (1997), 149–157.Google Scholar
[6]Wojtaszczyk, P., Banach spaces for analysts (Cambridge University Press, Cambridge, 1991).CrossRefGoogle Scholar
[7]Yen, N.D. and Kim, B.T., ‘Linear operators satisfying the assumptions of some generalized Lax-Milgram theorems’, Acta Math. Vietnam. 26 (2001), 407–417.Google Scholar