Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 18 (2023), 107 -- 121

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This work is licensed under a Creative Commons Attribution 4.0 International License.

POSITIVE COHEN p-NUCLEAR m-HOMOGENEOUS POLYNOMIALS

Asma Hammou, Amar Belacel, Amar Bougoutaia and Abdelmoumen Tiaiba

Abstract. In this paper we introduce the concept of positive Cohen p-nuclear polynomials between Banach lattice spaces. We give an analogue to Pietsch domination theorem and we study some properties concerning this notion.

2020 Mathematics Subject Classification: 46A20; 46A32; 46B42; 47A07; 47B10; 47B65.
Keywords: Banach lattice; Positive Cohen p-nuclear polynomials; Positive Cohen strongly p-summing polynomials.

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References

  1. D. Achour, A. Alouani, On multilinear generalizations of the concept of nuclear operators, Colloquium Mathematicae. 120(2010), 85 - 102. MR2652609. Zbl 1219.47095.

  2. D. Achour, A. Alouani, P. Rueda, E. A. S. Pérez, Tensor Characterizations of Summing Polynomials, Mediterranean Journal of Mathematics. 15(2018), 1-12. MR3803740. Zbl 1482.47031.

  3. D. Achour, A. Belacel, Domination and factorization theorems for positive strongly p-summing operators, Positivity. 18(2014), 785-804. MR3275367. Zbl 1328.47020.

  4. O. Blasco, A class of operators from a Banach lattice into a Banach space, Collect. Math. 37(1986), 13-22. MR0882789. Zbl 0619.47019.

  5. A. Bougoutaia, A. Belacel, H. Hamdi, Domination and Kwapien’s factorization theorems for positive Cohen p-nuclear m-linear operators, Moroccan J. of Pure and Appl. Anal. 7(2021), 100–115.

  6. Q. Bu, G. Buskes, Polynomials on Banach lattices and positive tensor products, J. Math. Anal. Appl. 388(2012), 845-862. MR2869792. Zbl 1245.46035.

  7. J. S. Cohen, Absolutely p-summing, p-nuclear operators and their conjugates, Math. Ann. 201(1973), 177–201. MR0370245. Zbl 0233.47019.

  8. D. H. Fremlin, Tensor products of Banach lattices, Math. Ann. 211(1974), 87–106. MR0367620. Zbl 0272.46050.

  9. D. Ji, K. Navoyan, Q. Bu Complementation in the Fremlin vector lattice symmetric tensor products-II, Annals of Functional Analysis 11(2020), 47–61. MR4091406. Zbl 1445.46052.

  10. H. Hamdi, S. G. Hernandez, A. Belacel, D. Ouchenane, S. A. Zubair, Cohen Positive Strongly p-Summing and p-dominated m-homogeneous polynomials, Journal of Mathematics. 2021(2021), 1-18. MR4341498.

  11. L. Mezrag, K. Saadi, Inclusion theorems for Cohen strongly summing multilinear operators, Bull. Belg. Math. Soc. Simon Stevin. 16(2009), 1-11. MR2498954. Zbl 1176.47047.

  12. D. Pellegrino, J. Santos, J. B. Seoane-Sepúlvzda, Some techniques on nonlinear analysis and applications, Sciverse Science Direct advaces in Mathematics. 229(2012), 1235-1265. MR2855092. Zbl 1248.47024.

  13. A. Pietsch, Ideals of multilinear functionals, In: Proceedings of the Second International Conference on Operator Algebras, Ideals, and Their Applications in Theoretical Physics, Teubner-Texte, Leipzig, 1983, 185–99. MR0763541. Zbl 0562.47037.

  14. R. A. Ryan, Introduction to tensor products of Banach spaces, Springer Monographs in Mathematics, 2002. MR1888309. Zbl 1090.46001.

  15. H. Schaefer, Banach lattices and Positive Operators, Springer-Verlag, New York, 1974. MR0423039. Zbl 0296.47023.



Asma Hammou
Department of Mathematics, M’sila University, Algeria,
Département Mathématiques, Ecole Normale Supérieure de Laghouat, Algérie.
e-mail: asma.hammou@univ-msila.dz, a.hammou@ens-lagh.dz

Amar Belacel
Laboratory of Pure and Applied Mathematics (LPAM), University of Laghouat, Algeria.
e-mail: amarbelacel@yahoo.fr

Amar Bougoutaia
Laboratory of Pure and Applied Mathematics (LPAM), University of Laghouat, Algeria.,
e-mail: amarbou28@gmail.com

Abdelmoumen Tiaiba
Renewable Materials and Energies Laboratory "LMER" of the university of M’sila. Algeria,
e-mail: abdelmoumen.tiaiba@univ-msila.dz

http://www.utgjiu.ro/math/sma