Publication:
Some techniques on nonlinear analysis and applications

Loading...
Thumbnail Image
Full text at PDC
Publication Date
2012
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsvier
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
In this paper we present two different results in the context of nonlinear analysis. The first one is essentially a nonlinear technique that, in view of its strong generality, may be useful in different practical problems. The second result, more technical, but also connected to the first one, is an extension of the well known Pietsch Domination Theorem. The last decade witnessed the birth of different families of Pietsch Domination-type results and some attempts of unification. Our result, that we call "full general Pietsch Domination Theorem" is potentially a definitive Pietsch Domination Theorem which unifies the previous versions and delimits what can be proved in this line. The connections to the recent notion of weighted summability are traced.
Description
UCM subjects
Análisis funcional y teoría de operadores
Unesco subjects
Keywords
Citation
D. Achour, L. Mezrag, On the Cohen strongly p-summing multilinear operators, J. Math. Anal. Appl. 327 (2007)550–563. M. Acosta, D. García, M. Maestre, A multilinear Lindenstrauss theorem, J. Funct. Anal. 235 (2006) 122–136. F. Albiac, N. Kalton, Topics in Banach Space Theory,Springer-Verlag, 2005. R. Aron, J. Globevnik, Analytic Functions on c0, Rev.Mat.Univ. Complut. Madrid 2 (1989) 27–33. S. Banach, Théorie des opérations linéaires, PWN, 1932. G. Bennett, Inclusion mappings between p spaces, J. Funct. Anal. 12 (1973) 420–427. G. Bennett, Schur multipliers, Duke Math. J. 44 (1977) 609–639. H.F. Bohnenblust, E. Hille, On the absolute convergence of Dirichlet series, Ann. of Math. 32 (1931) 600–622. F. Bombal, D. Peréz-García, I. Villanueva, Multilinear extensions of Grothendieck’s theorem, Q. J. Math. 55 (2004)441–450. G. Botelho, H.-A. Braunss, H. Junek, D. Pellegrino,Holomorphy types and ideals of multilinear mappings, Studia Math. 177 (2006) 43–65. G. Botelho, C. Michels, D. Pellegrino, Complex interpolation and summability properties of multilinear operators,Rev. Mat. Complut. 23 (2010) 139–161. G. Botelho, D. Pellegrino, Absolutely summing operators on Banach spaces with no unconditional basis, J. Math.Anal.Appl. 321 (2006) 50–58. G. Botelho, D. Pellegrino, Coincidence situations for absolutely summing non-linear mappings, Port. Math. 64 (2007) 175–191. G. Botelho, D. Pellegrino, When every multilinear mapping is multiple summing, Math. Nachr. 282 (2009) 1414–1422. G. Botelho, D. Pellegrino, P. Rueda, Pietsch’s factorization theorem for dominated polynomials, J. Funct. Anal. 243 (2007) 257–269. G. Botelho, D. Pellegrino, P. Rueda, A nonlinear Pietsch Domination Theorem, Monatsh. Math. 158 (2009) 247–257. G. Botelho, D. Pellegrino, P. Rueda, A unified Pietsch Domination Theorem, J. Math. Anal. Appl. 365 (2010)269–276. G. Botelho, D. Pellegrino, P. Rueda, Cotype and absolutely summing linear operators, Math. Z. 267 (2011) 1–7. E. Çaliskan, D. Pellegrino, On the multilinear generalizations of the concept of absolutely summing operators,Rocky Mountain J. Math. 37 (2007) 1137–1154. B. Carl, Absolut (p, 1)-summierende identische operatoren von lu nach lv , Math. Nachr. 63 (1974) 353–360. A. Defant, K. Floret, Tensor Norms and Operator Ideals, North-Holland Math. Stud., vol. 176, North-Holland,Amsterdam, 1993. A. Defant, D. García, M. Maestre, D. Pérez-García, Bohr’s strip for vector valued Dirichlet series, Math. Ann. 342 (2008) 533–555. A. Defant, D. Pérez-García, A tensor norm preserving unconditionality for Lp-spaces, Trans. Amer. Math. Soc. 360 (2008) 3287–3306. A. Defant, P. Sevilla-Peris, A new multilinear insight on Littlewood’s 4/3-inequality, J. Funct. Anal. 256 (2009)1642–1664. J. Diestel, An elementary characterization of absolutely summing operators, Math. Ann. 196 (1972) 101–105. J. Diestel, J. Fourie, J. Swart, The Metric Theory of Tensor Products – Grothendieck’s Résumé Revisited, American Mathematical Society, 2008. J. Diestel, H. Jarchow, A. Tonge, Absolutely Summing Operators, Cambridge University Press, 1995. V. Dimant, Strongly p-summing multilinear mappings, J.Math. Anal. Appl. 278 (2003) 182–193. S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, 1999. E. Dubinsky, A. Pełczynski, H.P. Rosenthal, On Banach spaces X for which Π2(L∞,X) = B(L∞,X), Studia Math. 44 (1972) 617–648. A. Dvoretzky, C.A. Rogers, Absolute and unconditional convergence in normed linear spaces, Proc. Natl. Acad.Sci. USA 36 (1950) 192–197. J. Farmer, W.B. Johnson, Lipschitz p-summing operators,Proc. Amer. Math. Soc. 137 (2009) 2989–2995. S. Geiss, Ideale multilinearer Abbildungen, Diplomarbeit,1985. A. Grothendieck, Résumé de la théorie metrique des produits tensoriels topologiques, Bol. Soc. Mat. São Paulo 8 (1953/1956) 1–79. A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Acad. Math. Soc. 16 (1955). G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities,Cambridge University Press, 1952. J. Hoffmann-Jørgensen, Sums of independent Banach space valued random variables, Studia Math. 52 (1974) 159–186. H. Jarchow, C. Palazuelos, D. Pérez-García, I. Villanueva, Hahn–Banach extension of multilinear forms and summability,J. Math. Anal. Appl. 336 (2007) 1161–1177. H. Junek, M.C. Matos, D. Pellegrino, Inclusion theorems for absolutely summing holomorphic mappings, Proc.Amer. Math. Soc. 136 (2008) 3983–3991. T. Kühn, M. Mastyło, Products of operator ideals and extensions of Schatten classes, Math. Nachr. 283 (2010)891–901. T. Kühn, M. Mastyło, Weyl numbers and eigenvalues of abstract summing operators, J. Math. Anal. Appl. 369 (2010) 408–422. S. Kwapien, Some remarks on (p, q)-summing operators in lp spaces, Studia Math. 29 (1968) 327–337. S. Kwapien, Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients, Studia Math. 44 (1972) 583–595. J. Lindenstrauss, A. Pełczynski, Absolutely summing operators in Lp spaces and their applications, StudiaMath.29(1968) 275–326. J.E. Littlewood, On bounded bilinear forms in an infinite number of variables, Quart. J. Oxford Ser. 1 (1930) 164–174. M.S. Macphail, Absolute and unconditional convergence,Bull. Amer. Math. Soc. 53 (1947) 121–123. F. Martínez-Giménez, E.A. Sánchez-Pérez, Vector measure range duality and factorizations of (D,p)-summing operators from Banach function spaces, Bull. Braz. Math. Soc. (N.S.) 35 (2004) 51–69
Collections