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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.14 no.1 Temuco  2012

http://dx.doi.org/10.4067/S0719-06462012000100003 

CUBO A Mathematical Journal Vol.14, N° 01, (21-27). March 2012

 

Remarks on cotype and absolutely summing multilinear operators

 

A. Thiago Bernardino

UFRN/CERES, Centro de E Centro de Ensino Superior do Serió, Rua Joaquim Gregório, S/N, 59300-000, Caicó- RN, Brazil, email: thiagobernardino@yahoo.com.br


ABSTRACT

In this short note we present some new results concerning cotype and absolutely summing multilinear operators, extending recent results from different authors.

Keywords and Phrases: Absolutely p-summing multilinear operators, cotype.


RESUMEN

En esta nota presentamos nuevos resultados sobre cotipo y suma absoluta de operadores multilineales, extendiendo resultados recientes de diferentes autores.

2010 AMS Mathematics Subject Classification: 46G25,47B10.

 

References

[1] R. Alencar and M. C. Matos, Some classes of multilinear mappings between Banach spaces, Publicaciones del Departamento de Análisis Matemático 12, Universidad Complutense Madrid, (1989).

[2] A. Thiago Bernardino and D. Pellegrino, Some remarks on absolutely summing multilinear operators, arXiv:1101.2119v2.

[3] O. Blasco, G. Botelho, D. Pellegrino and P. Rueda, Lifting summability properties for multilinear mappings, preprint.

[4] G. Botelho, Cotype and absolutely summing multilinear mappings and homogeneous polynomials, Proc. Roy. Irish Acad Sect. A 97 (1997), 145-153.

[5] G. Botelho, C. Michels and D. Pellegrino, Complex interpolation and summability properties of multilinear operators, Rev. Matem. Complut. 23 (2010), 139-161.

[6] G. Botelho, D. Pellegrino and P. Rueda, Cotype and absolutely summing linear operators, Mathematische Zeitschrift, 267 (2011), 1-7.

[7] E. Caliskan and D. M. Pellegrino, On the multilinear generalizations of the concept of absolutely summing operators, Rocky Mount. J. Math. 37 (2007), 1137-1154.

[8] A. Defant, D. Popa and U. Schwarting, Coordenatewise multiple summing operators on Banach spaces, J. Funct. Anal. 259 (2010), 220-242.

[9] J. Diestel, H. Jarchow and A. Tonge, Absolutely summing operators, Cambridge University Press, 1995.

[10] H. Junek, M.C. Matos and D. Pellegrino, Inclusion theorems for absolutely summing holomorphic mappings, Proc. Amer. Math. Soc. 136 (2008), 3983-3991.

[11] Y. Meléndez and A. Tonge, Polynomials and the Pietsch Domination Theorem, Proc. Roy. Irish Acad Sect. A 99 (1999), 195-212.

[12] D. Pellegrino, Cotype and absolutely summing homogeneous polynomials in Lp spaces, Studia Math. 157 (2003), 121-131.

[13] D. Pellegrino, Cotype and nonlinear absolutely summing mappings, Math. Proc. Roy. Irish Acad., 105A (2005), 75-91.

[14] D. Pellegrino and J. Santos, Absolutely summing operators: a panorama, Quaestiones Mathematicae 34 (2011), 447-478.

[15] D. Popa, Reverse inclusions for multiple summing operators, J. Math. Anal. Appl. 350 (2009), 360-368.

[16] D. Popa, Multilinear variants of Maurey and Pietsch theorems and applications, J. Math. Anal. Appl. 368 (2010) 157-168.


Received: January 2011. Revised: February 2011.

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