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‘POSITIVELY HOMOGENEOUS LATTICE HOMOMORPHISMS BETWEEN RIESZ SPACES NEED NOT BE LINEAR’

Part of: Special classes of linear operators Topological linear spaces and related structures

Published online by Cambridge University Press:  08 July 2016

FETHI BEN AMOR
FETHI BEN AMOR*
Affiliation:
Research Laboratory LATAO, Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El-Manar, 2092 El-Manar, Tunisia email fethi.benamor@ipest.rnu.tn
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Abstract

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This note furnishes an example showing that the main result (Theorem 4) in Toumi [‘When lattice homomorphisms of Archimedean vector lattices are Riesz homomorphisms’, J. Aust. Math. Soc. 87 (2009), 263–273] is false.

Keywords

lattice homomorphism

MSC classification

Primary: 46A40: Ordered topological linear spaces, vector lattices
Secondary: 47B65: Positive operators and order-bounded operators
Type
Article Commentary
Information
Journal of the Australian Mathematical Society , Volume 102 , Issue 3 , June 2017 , pp. 444 - 445
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Ercan, Z. and Wickstead, A. W., ‘When a lattice homomorphism is a Riesz homomorphism’, Math. Nachr. 279 (2006), 1024–1027.CrossRefGoogle Scholar
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Mena, R. and Roth, B., ‘Homomorphisms of lattices of continuous functions’, Proc. Amer. Math. Soc. 71 (1978), 11–12.Google Scholar
Thanh, D. T., ‘A generalization of a theorem of R. Mena and R. Roth’, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 34 (1992), 167–171.Google Scholar
Toumi, M. A., ‘When lattice homomorphisms of Archimedean vector lattices are Riesz homomorphisms’, J. Aust. Math. Soc. 87 (2009), 263–273.Google Scholar