Abstract
The concepts of orthomorphisms and central operators are well known and established in the theory of linear operators on vector lattices. In this work we introduce versions of the definitions of orthomorphisms and of central operators for nonlinear operators. We investigate the order structure of the corresponding spaces of these nonlinear operators. If the vector lattice is Dedekind complete, then both spaces are also Dedekind complete vector lattices, but in general they are not even vector lattices.
This author gratefully acknowledges the support of TUBITAK (the Scientific and Technical Research Council of Turkey) during the preparation of this work.
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References
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© 1998 Springer-Verlag Berlin · Heidelberg
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Ercan, Z., Wickstead, A.W. (1998). Towards a Theory of Nonlinear Orthomorphisms. In: Abramovich, Y., Avgerinos, E., Yannelis, N.C. (eds) Functional Analysis and Economic Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72222-6_6
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DOI: https://doi.org/10.1007/978-3-642-72222-6_6
Publisher Name: Springer, Berlin, Heidelberg
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