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1998 | 131 | 2 | 155-165
Tytuł artykułu

On multilinear mappings attaining their norms.

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show, for any Banach spaces X and Y, the denseness of the set of bilinear forms on X × Y whose third Arens transpose attains its norm. We also prove the denseness of the set of norm attaining multilinear mappings in the class of multilinear mappings which are weakly continuous on bounded sets, under some additional assumptions on the Banach spaces, and give several examples of classical spaces satisfying these hypotheses.
Słowa kluczowe
Czasopismo
Rocznik
Tom
131
Numer
2
Strony
155-165
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-09-22
poprawiono
1998-03-02
Twórcy
  • Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada 18071, Granada, Spain, dacosta@goliat.ugr.es
Bibliografia
  • [1] M. D. Acosta, F. J. Aguirre and R. Payá, There is no bilinear Bishop-Phelps Theorem, Israel J. Math. 93 (1996), 221-228.
  • [2] F. Aguirre, Algunos problemas de optimización en dimensión infinita: aplicaciones lineales y multilineales que alcanzan su norma, doctoral dissertation, University of Granada, 1996.
  • [3] R. Arens, Operations induced in function classes, Monatsh. Math. 55 (1951), 1-19.
  • [4] R. Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839-848.
  • [5] R. M. Aron, C. Finet and E. Werner, Some remarks on norm-attaining n-linear forms, in: Function Spaces, K. Jarosz (ed.), Lecture Notes in Pure and Appl. Math. 172, Marcel Dekker, New York, 1995, 19-28.
  • [6] R. M. Aron, C. Hervés and M. Valdivia, Weakly continuous mappings on Banach spaces, J. Funct. Anal. 52 (1983), 189-204.
  • [7] J. M. Baker, A note on compact operators which attain their norm, Pacific J. Math. 82 (1979), 319-321.
  • [8] Y. S. Choi, Norm attaining bilinear forms on $L_1[0,1]$, J. Math. Anal. Appl. 211 (1997), 295-300.
  • [9] Y. S. Choi and S. G. Kim, Norm or numerical radius attaining multilinear mappings and polynomials, J. London Math. Soc. 54 (1996), 135-147.
  • [10] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977.
  • [11] V. Dimant and I. Zalduendo, Bases in spaces of multilinear forms over Banach spaces, J. Math. Anal. Appl. 200 (1996), 548-566.
  • [12] T. W. Gamelin, Analytic functions on Banach spaces, in: Complex Potential Theory, P. M. Gauthier and G. Sabidussi (eds.), Kluwer, 1994, 187-233.
  • [13] R. Gonzalo and J. Jaramillo, Compact polynomials between Banach spaces, Extracta Math. 8 (1993), 42-48.
  • [14] A. Grothendieck, Sur les applications linéaires faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953), 129-173.
  • [15] J. Gutierrez, J. Jaramillo and J. G. Llavona, Polynomials and geometry of Banach spaces, Extracta Math. 10 (1995), 79-114.
  • [16] M. Jiménez Sevilla and R. Payá, Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces, Studia Math. 127 (1998), 99-112.
  • [17] J. Johnson and J. Wolfe, Norm attaining operators, ibid. 65 (1979), 7-19.
  • [18] D. Leung, Uniform convergence of operators and Grothendieck spaces with the Dunford-Pettis property, Math. Z. 197 (1988), 21-32.
  • [19] J. Lindenstrauss, On operators which attain their norm, Israel J. Math. 1 (1963), 139-148.
  • [20] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I: Sequence Spaces, Springer, Berlin, 1977.
  • [21] P A. Pełczyński, A property of multilinear operations, Studia Math. 16 (1957), 173-182.
  • [22] R. A. Poliquin and V. Zizler, Optimization of convex functions on w*-convex sets, Manuscripta Math. 68 (1990), 249-270.
  • [23] V. Zizler, On some extremal problems in Banach spaces, Math. Scand. 32 (1973), 214-224.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv131i2p155bwm
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