Strongly Lipschitz up-Nuclear Operators

Belacel, Amar; Bey, Khedidja

doi:10.2478/mjpaa-2019-0002

Abstract

In this paper, we introduce the notion of strongly Lipschitz up-nuclear operators. Among other results, we prove an analog of the factorization theorem for these classes and characterize their conjugates.

References

[1] D. Achour, P. Rueda, E.A. Sánchez-Pérez 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 and J. Eells Jr., On embedding uniform and topological spaces, Pacific J. Math., 6 (1956), 397-403.10.2140/pjm.1956.6.397
Search in Google Scholar Back to article
[3] A. Belacel and 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] D. Chen and 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
[5] J.S. Cohen, Absolutely p-summing, p-nuclear operators and their conjugates, Math. Ann., 201 (1973), 177-200.10.1007/BF01427941
Search in Google Scholar Back to article
[6] A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holl. Math. Stud., vol. 176, North-Holland Publishing Co., Amsterdam, (1993).
Search in Google Scholar Back to article
[7] J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge University Press, (1995).10.1017/CBO9780511526138
Search in Google Scholar Back to article
[8] J.D. Farmer and 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
[9] D.J.H. Garling: Inequalities, A journey into Linear Analysis, Cambridge University Press, (2007).10.1017/CBO9780511755217
Search in Google Scholar Back to article
[10] H. Hogbe-Nlend and V. B. Moscatelli, Nuclear and Conuclear Spaces, North-52. North-Holland Publishing Company, (1981).
Search in Google Scholar Back to article
[11] R. Khalil, A. Yousef, Isometries of P-nuclear operator spaces, J. Comput. Anal. Appl. 16(2)(2014), 368-374.
Search in Google Scholar Back to article
[12] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Tome 1. Sequence Springer-Verlag, (1977).10.1007/978-3-642-66557-8_1
Search in Google Scholar Back to article
[13] K. Miyazaki, (p,q)-Nuclear and (p,q)-Integral Operators, Hiroshima Math. J., 4 (1974), 99-132.10.32917/hmj/1206137156
Search in Google Scholar Back to article
[14] A. Persson, On some properties of p-nuclear and p-integral operators, Studia Math., (1969), 113-222.10.4064/sm-33-2-213-222
Search in Google Scholar Back to article
[15] A. Pietsch, Operator ideals, North-Holland Publishing Company, (1980).
Search in Google Scholar Back to article
[16] O.I. Reinov, On Linear operators with p-nuclear adjoints, Math. FA, (2001).
Search in Google Scholar Back to article
[17] S. Reisner, A factoriztion theorem in Banach lattices and its application to Lorentz spaces, Annales de l’institut Fourier, tome 31, n 0 1, p. (1981), 239-255.10.5802/aif.825
Search in Google Scholar Back to article
[18] I. Sawashima, Methods of Lipschitz Duals, Lecture Notes in Econom. and Math. Systems, vol. 419, Springer Verlag, pp. (1975), 247-259.
Search in Google Scholar Back to article
[19] R. Yahi, D. Achour and P. Rueda, Absolutely summing Lipschitz conjugates, Mediterr. J. Math., 13 (2016), 1949-1961.10.1007/s00009-015-0623-2
Search in Google Scholar Back to article
[20] N. Weaver, Lipschitz Algebras, World Scientific Publishing Co., Singapore, (1999).10.1142/4100
Search in Google Scholar Back to article

Strongly Lipschitz up-Nuclear Operators

Abstract

Paradigm

My account