Lipschitz (q, p, E)-summing operators on injective Lipschitz tensor products of spaces
References
- [1] D. Achour, E.Dahia and M. A. S. Saleh, Multilinear mixing operators and Lipschitz mixing operator ideals, Operators and matrices. 12 (4) (2018), 903-931.<a href="https://doi.org/10.7153/oam-2018-12-55" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.7153/oam-2018-12-55</a>
- [2] D. Achour, E. Dahia and P. Turco, The Lipschitz injective hull of Lipschitz operator ideals and applications, Banach J. Math. Anal. (2020). <a href="https://doi.org/10.1007/s43037-020-00060-3.10.1007/s43037-020-00060-3" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">https://doi.org/10.1007/s43037-020-00060-3.10.1007/s43037-020-00060-3</a>
- [3] D. Achour, P. Rueda, and R. Yahi, (p, σ)-Absolutely Lipschitz operators, Ann. Funct. Anal. 8 (1) (2017), 38-50.<a href="https://doi.org/10.1215/20088752-3720614" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1215/20088752-3720614</a>
- [4] O. Blasco and T. Signes, Remarks on (q, p, Y)-summing operators, Quaestiones Mathematicae. 252002, 97-103.<a href="https://doi.org/10.2989/16073600309486047" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.2989/16073600309486047</a>
- [5] G. Botelho, D. Pellegrino and P. Rueda, A unified Pietsch Domination Theorem, J. Math. Anal. Appl. 365 2010, 269-276.<a href="https://doi.org/10.1016/j.jmaa.2009.10.025" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/j.jmaa.2009.10.025</a>
- [6] M. G. Cabrera-Padilla, J. A. Chàvez-Doménguez, A. Jiménez-Vargas and M. Villegas-Vallecillos, Lipschitz Tensor Product, Khayyam J. Math. 1 2015, 185–218.
- [7] J. A. Chávez-Domínguez, Lipschitz (q, p)-mixing operators, Proc. Amer. Math. Soc. 140 2012, 3101–3115.<a href="https://doi.org/10.1090/S0002-9939-2011-11140-7" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1090/S0002-9939-2011-11140-7</a>
- [8] D. Chen and B. Zheng, Lipschitz p-integral operators and Lipschitz p-nuclear operators, Nonlinear Analysis 75 2012, 5270-5282.<a href="https://doi.org/10.1016/j.na.2012.04.044" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/j.na.2012.04.044</a>
- [9] J. D. Farmer and W. B. Johnson, Lipschitz p-summing operators, Proc. Amer. Math. Soc. 137 (9) (2009), 2989–2995.<a href="https://doi.org/10.1090/S0002-9939-09-09865-7" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1090/S0002-9939-09-09865-7</a>
- [10] W. B. Johnson and G. Schechtman, Diamond graphs and super-reflexivity, J. Topol. Anal. 1 (2) (2009), 177–189.<a href="https://doi.org/10.1142/S1793525309000114" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1142/S1793525309000114</a>
- [11] S.V.Kislyakov, Absolutely summing operators on disk algebra, St. Petrsburg Math. J. 3(4) (1992), 705-774.
- [12] B.Maurey, Rappels sur les opérateurs sommants et radonifiants, Séminaire d’analyse fonctionnelle (Polytechnique). (1) (1973-1974), 1-9.
- [13] L.Mezrag and A.Tallab, On Lipschitz τ (p) −summing operators, Colloq. Math. 147 (1) (2017), 95-114.<a href="https://doi.org/10.4064/cm6763-3-2016" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.4064/cm6763-3-2016</a>
- [14] S. Montgomery-Smith and P. Saab, p -summing operators on injective tensor products of spaces, Proc. Roy. Soc. Edinburgh Sect. 120A 1992, no. 3-4, 283–296.<a href="https://doi.org/10.1017/S0308210500032145" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1017/S0308210500032145</a>
- [15] D. Pellegrino and J. Santos, A general Pietsch Domination Theorem, J. Math. Anal. Appl. 375 2011, 371-374.<a href="https://doi.org/10.1016/j.jmaa.2010.08.019" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/j.jmaa.2010.08.019</a>
- [16] D. Pellegrino, J. Santos and J.B. Seoane-Sepúlveda, Some techniques on nonlinear analysis and applications, Adv. Math. 229 2012, 1235–1265.<a href="https://doi.org/10.1016/j.aim.2011.09.014" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/j.aim.2011.09.014</a>
- [17] A. Pietsch, Operator Ideals, Deutsch. Verlag Wiss., Berlin, 1978; North–Holland, Amsterdam–London–New York–Tokyo, 1980.
- [18] M. A. S. Saleh, New types of Lipschitz summing maps between metric spaces, Math. Nachr. 290 2017, 1347–1373.<a href="https://doi.org/10.1002/mana.201500020" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1002/mana.201500020</a>
- [19] N. Weaver, Lipschitz Algebras, World Scientific, Singapore 1999.<a href="https://doi.org/10.1142/4100" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1142/4100</a>
DOI: https://doi.org/10.2478/mjpaa-2020-0010 | Journal eISSN: 2351-8227
Language: English
Page range: 127 - 142
Submitted on: Feb 23, 2020
Accepted on: May 6, 2020
Published on: May 29, 2020
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 3 times per year
Related subjects:
© 2020 Abdelhamid Tallab, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.