Some results about Lipschitz p-Nuclear Operators

Bey, Khedidja; Belacel, Amar

doi:10.2478/mjpaa-2021-0025

Abstract

The aim of this paper is to study the onto isometries of the space of strongly Lipschitz p-nuclear operators, introduced by D. Chen and B. Zheng (Nonlinear Anal.,75, 2012). We give some new results about such isometrics and we focus, in particular, on the case F = ℓ_p*.

References

[1] D. Achour, P. Rueda, E.A. Snchez-Prez, and R. Yahi, Lipschitz operator ideals and the approximation property, J. Math. Anal. Appl., 436 (2016), 217-236.10.1016/j.jmaa.2015.11.050
Search in Google Scholar Back to article
[2] R.F. Arens, J. Jr. Eells, On embedding uniform and topological spaces, Pac. J. Math., 6 (1956), 397-403.10.2140/pjm.1956.6.397
Search in Google Scholar Back to article
[3] A. Belacel, D. Chen, Lipschitz (p,r,s)-integral operators and Lipschitz (p,r,s)-nuclear operators, J. Math. Anal. Appl. 461 (2018), 1115-1137.10.1016/j.jmaa.2018.01.056
Search in Google Scholar Back to article
[4] A. Belacel and Kh. Bey, Strongly Lipschitz up-nuclear operators, Moroccan J. of Pure and Appl. Anal. 5(1) (2019), 22-30.10.2478/mjpaa-2019-0002
Search in Google Scholar Back to article
[5] M.G. Cabrera-Padilla, A. Jimnez-Vargas, and M. Villegas-Valle Cillos, A survey on isometries between Lipschitz spaces. The Moroccan Andalusian Meeting on algebras and thier applications, (2018), 51-88.10.1007/978-3-030-35256-1_3
Search in Google Scholar Back to article
[6] J.A. Chávez-Domínguez, Duality for Lipschitz p-summing operators, J. Funct Anal., 261 (2011), 387-407.10.1016/j.jfa.2011.03.013
Search in Google Scholar Back to article
[7] J.A. Chávez-Domínguez, Lipschitz (q, p)-mixing operators, Proc. Am. Math. Soc., 140 (2012), 3101-3115.10.1090/S0002-9939-2011-11140-7
Search in Google Scholar Back to article
[8] D. Chen, B. Zheng, Remarks on Lipschitz p-summing operators, Proc. Am. Math. Soc., 139 (8) (2011), 2891-2898.10.1090/S0002-9939-2011-10720-2
Search in Google Scholar Back to article
[9] D. Chen, B. Zheng, Lipschitz p-integral operators and Lipschitz p-nuclear operators, Nonlinear Anal., 75 (2012), 5270-5282.10.1016/j.na.2012.04.044
Search in Google Scholar Back to article
[10] J. Diestel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge University Press, Cambridge, (1995).10.1017/CBO9780511526138
Search in Google Scholar Back to article
[11] J.D. Farmer, W.B, Johnson, Lipschitz p-summing operators. Proc. Am. Math. Soc., 137(9) (2009), 2989-2995.10.1090/S0002-9939-09-09865-7
Search in Google Scholar Back to article
[12] A. Jimnez-Vargas, J.M. Sepulcre, and M. Villegas-Vallecillos, Lipschitz compact operators, J. Math. Anal. Appl., 415(2) (2014), 889-901.10.1016/j.jmaa.2014.02.012
Search in Google Scholar Back to article
[13] R. Khalil, I. Adarwi, Isometries of p-nuclear type operators, J. Math. Comput. Sci, 5 (2015), 91-98.
Search in Google Scholar Back to article
[14] R. Khalil, A. Salah, Isometries of certains operator spaces Proc. An. Math.Soc, 2003, 14731481.10.1090/S0002-9939-03-07210-1
Search in Google Scholar Back to article
[15] R. Khalil, A. Yousef, Isometries of p-nuclear operators, J. Comput. Anal. Appl., 16(2) (2014), 368-374.
Search in Google Scholar Back to article
[16] A. Pietsch, Operator ideals, North-Holland publishing company, Amsterdam, 1980.
Search in Google Scholar Back to article
[17] I. Sawashima, Methods of Lipschitz Duals, Lecture Notes Ec. Math Sust, vol. 419 (1975), 247-259.
Search in Google Scholar Back to article
[18] N. Weaver, Lipschitz Algebras, World Scientific Publishing Co., Singapore, (1999).10.1142/4100
Search in Google Scholar Back to article

Some results about Lipschitz p-Nuclear Operators

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