Abstract
The paper aims to examine the problem of characterization and representation of order bounded multilinear operators between vector lattices which may be expressed as sums of disjointness preserving multilinear operators.
Similar content being viewed by others
References
Abramovich, Y.A., Kitover, A.K.: Inverses and regularity of disjointness preserving operators. Indag. Math. N. S. 13(2), 143–167 (2002)
Aliprantis, C.D., Burkinshaw, O.: Positive Operators. Academic Press Inc., London (1985)
Bernau, S.J.: Sums and extensions of vector lattice homomorphisms. Acta Appl. Math. 27, 33–45 (1992)
Bernau, S.J., Huijsmans, C.B., de Pagter, B.: Sums of lattice homomorphisms. Proc. Am. Math. Soc. 115, 151–156 (1992)
Boulabiar, K.: Products in almost \(f\)-algebras. Comment. Math. Univ. Carolin 41(4), 747–759 (2000)
Boulabiar, K.: Some aspects of Riesz multimorphisms. Indag. Mathem. N.S. 13(4), 419–432 (2002)
Boulabiar, K.: Recent trends on order bounded disjointness preserving operators. Irish Math. Soc. Bull. 62, 43–69 (2008)
Boulabiar, K., Buskes, G.: Vector lattice powers: \(f\)-algebras and functional calculus. Commun. Algebra 34(4), 1435–1442 (2006)
Bu, Q., Buskes, G., Kusraev, A.G.: Bilinear Maps on Products of Vector Lattices. A Survey, Positivity, pp. 97–126. Birkhaüser, Boston (2007)
Buskes Jr., G., Page, R.Y.: A note on bi-orthomorphisms, operator theory. Adv. Appl. 201, 99–107 (2009)
Buskes, G., de Pagter, B., van Rooij, A.: Functional calculus in Riesz spaces. Indag. Math. N.S. 4(2), 423–436 (1991)
Buskes, G., van Rooij, A.: Almost \(f\)-algebras: commutativity and the Cauchy–Schwarz inequality. Positivity 4(3), 227–231 (2000)
Buskes, G., van Rooij, A.: Squares of Riesz spaces. Rocky Mt. J. Math. 31(1), 45–56 (2001)
Buskes, G., van Rooij, A.: Bounded variation and tensor products of Banach lattices. Positivity 7, 47–59 (2003)
Carothers, D.C., Feldman, W.A.: Sums of homomorphisms on Banach lattices. J. Opera. Theory 24(2), 337–349 (1990)
Fremlin, D.H.: Tensor products of Archimedean vector lattices. Am. J. Math. 94, 778–798 (1972)
Gutman, A.E.: Disjointness preserving operators. In: Kutateladze, S.S. (ed.) Vector Lattices and Integral Operators, pp. 361–454. Kluwer Academic Publishers, Dordrecht (1996)
Kusraev, A.G.: Dominated Operators. Kluwer Academic Publishers, Dordrecht (2000)
Kusraev, A.G., Kusraeva, Z.A.: Factorization of order bounded disjointness preserving multilinear operators. In: Modern Methods in Operator Theory and Harmonic Analysis: OTHA 2018, Rostov-on-Don, Russia, April 22–27, Selected. Revised and Extended Contributions, pp. 217–23 (2019)
Kusraev, A.G., Kutateladze, S.S.: Boolean Valued Analysis: Selected Topics. Vladikavkaz Scientific Center Press, Vladikavkaz (2014)
Kusraev, A.G., Tabuev, S.N.: On multiplicative representation of disjointness preserving bilinear operators. Siber. Math. J. 49(2), 357–366 (2008)
Kusraev, A.G., Tabuev, S.N.: On disjointness preserving bilinear operators. Vladikavkaz Math. J. 6(1), 58–70 (2004)
Kusraeva, Z.A.: Representation of orthogonally additive polynomials. Sib. Math. J. 52(2), 248–255 (2011)
Kusraeva, Z.A.: Characterization and multiplicative representation of homogeneous disjointness preserving polynomials. Vladikavkaz Math. J. 18(1), 51–62 (2016)
Meyer-Nieberg, P.: Banach Lattices. Springer, Berlin (1991)
Radnaev, V.A.: On \(n\)-disjoint operators. Siber Adv. Math. 7(4), 44–78 (1997)
Radnaev, V.A.: On Metric \(n\)-Indecomposability in Ordered Lattice Normed Spaces and Its Applications. Sobolev Institute Press, Novosibirsk (1997). PhD Thesis
Schep, A.R.: Factorization of positive multilinear maps. Ill. J. Math. 28(4), 579–591 (1984)
Acknowledgements
The author would like to thank the Reviewer for valuable remarks and useful suggestions, which led to an improvement of the manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The study was supported by Russian Foundation for Basic Research (Project No 18-31-00205).
Rights and permissions
About this article
Cite this article
Kusraeva, Z. Sums of disjointness preserving multilinear operators. Positivity 25, 669–678 (2021). https://doi.org/10.1007/s11117-020-00781-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11117-020-00781-7