Lipschitz integral operators represented by vector measures

• Dahia, Elhadj ^[1] ; Hamidi, Khaled ^[2]
  1. [1] Ecole Normale Supérieure de Bousaada
  2. [2] University of Mohamed El-Bachir El-Ibrahimi ; University of M’sila
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 22, Nº. 2, 2021, págs. 367-383
• Idioma: inglés
• DOI: 10.4995/agt.2021.15061
• Enlaces
  • Texto completo
• Resumen

  • In this paper we introduce the concept of Lipschitz Pietsch-p-integral mappings, (1≤p≤∞), between a metric space and a Banach space. We represent these mappings by an integral with respect to a vectormeasure defined on a suitable compact Hausdorff space, obtaining in this way a rich factorization theory through the classical Banach spaces C(K), L_p(μ,K) and L_∞(μ,K). Also we show that this type of operators fits in the theory of composition Banach Lipschitz operator ideals. For p=∞, we characterize the Lipschitz Pietsch-∞-integral mappings by a factorization schema through a weakly compact operator. Finally, the relationship between these mappings and some well known Lipschitz operators is given.

• Referencias bibliográficas
  • D. Achour, P. Rueda, E. A. Sánchez-Pérez and R. Yahi, Lipschitz operator ideals and the approximation property, J. Math. Anal. Appl. 436 (2016),...
  • R. F. Arens and J. Eels Jr., On embedding uniform and topological spaces, Pacific J. Math 6 (1956), 397-403. https://doi.org/10.2140/pjm.1956.6.397
  • 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....
  • Y. Benyamini and J. Lindenstrauss, Geometric nonlinear functional analysis, vol. 1, Amer. Math. Soc. Colloq. Publ., vol. 48, Amer. Math. Soc.,...
  • M. G. Cabrera-Padilla and A. Jiménez-Vargas, Lipschitz Grothendieck-integral operators, Banach J. Math. Anal. 9, no. 4 (2015), 34-57. https://doi.org/10.15352/bjma/09-4-3
  • C. S. Cardassi, Strictly p-integral and p-nuclear operators, in: Analyse harmonique: Groupe de travail sur les espaces de Banach invariants...
  • D. Chen and B. Zheng. Lipschitz p-integral operators and Lipschitz p-nuclear operators, Nonlinear Anal. 75 (2012), 5270-5282. https://doi.org/10.1016/j.na.2012.04.044
  • R. Cilia and J. M. Gutiérrez, Asplund Operators and p-Integral Polynomials, Mediterr. J. Math. 10 (2013), 1435-1459. https://doi.org/10.1007/s00009-013-0250-8
  • R. Cilia and J. M. Gutiérrez, Ideals of integral and r-factorable polynomials, Bol. Soc. Mat. Mexicana 14 (2008), 95-124.
  • J. Diestel, H. Jarchow and A. Tonge, Absolutely summing operators, Cambridge University Press, Cambridge, 1995. https://doi.org/10.1017/CBO9780511526138
  • J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys Monographs 15, American Mathematical Society, Providence RI, 1977. https://doi.org/10.1090/surv/015
  • N. Dunford and J. T. Schwartz, Linear Operators, Part I:General Theory, J. Wiley & Sons, New York, 1988.
  • J. D. Farmer and W. B. Johnson, Lipschitz p-summing operators, Proc. Amer. Math. Soc. 137, no. 9 (2009), 2989-2995. https://doi.org/10.1090/S0002-9939-09-09865-7
  • G. Godefroy, A survey on Lipschitz-free Banach spaces, Commentationes Mathematicae 55, no. 2 (2015), 89-118. https://doi.org/10.14708/cm.v55i2.1104
  • A. Jiménez-Vargas, J. M. Sepulcre and M. Villegas-Vallecillos, Lipschitz compact operators, J. Math. Anal. Appl. 415 (2014), 889-901. https://doi.org/10.1016/j.jmaa.2014.02.012
  • D. R. Lewis, Integration with respect to vector measures, Pacific J. Math. 33 (1970), 157-165. https://doi.org/10.2140/pjm.1970.33.157
  • S. Okada, W. J. Ricker and E. A. Sánchez-Pérez, Optimal domain and integral extension of operators acting in function spaces, Operator theory:...
  • A. Persson and A. Pietsch.p-nuklear und p-integrale Abbildungen in Banach räumen, Studia Math. 33 (1969), 19-62. https://doi.org/10.4064/sm-33-1-19-62
  • N. Weaver, Lipschitz Algebras, World Scientific Publishing Co., Singapore, 1999. https://doi.org/10.1142/4100