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1998 | 127 | 2 | 99-112
Tytuł artykułu

Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For each natural number N, we give an example of a Banach space X such that the set of norm attaining N-linear forms is dense in the space of all continuous N-linear forms on X, but there are continuous (N+1)-linear forms on X which cannot be approximated by norm attaining (N+1)-linear forms. Actually,X is the canonical predual of a suitable Lorentz sequence space. We also get the analogous result for homogeneous polynomials.
Czasopismo
Rocznik
Tom
127
Numer
2
Strony
99-112
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-09-17
poprawiono
1997-03-26
Twórcy
  • Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain,, marjim@sunam1.mat.ucm.es
autor
  • Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain, rpaya@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), 221-227.
  • [2] M. D. Acosta, F. J. Aguirre and R. Payá, A space by W. Gowers and new results on norm and numerical radius attaining operators, Acta Univ. Carolin. Math. Phys. 33 (1992), 5-14.
  • [3] F. J. Aguirre, Algunos problemas de optimización en dimensión infinita: aplicaciones lineales y multilineales que alcanzan su norma, Tesis Doctoral, Universidad de Granada, 1995.
  • [4] Z. Altshuler, P. G. Casazza and B.-L. Lin, On symmetric basic sequences in Lorentz sequence spaces, Israel J. Math. 15 (1973), 140-155.
  • [5] R. 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] E. R. Bishop and R. R. Phelps, A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc. 67 (1961), 97-98.
  • [7] P. G. Casazza and B.-L. Lin, On symmetric sequences in Lorentz sequence spaces II, Israel J. Math. 17 (1974), 191-218.
  • [8] Y. S. Choi, Norm attaining bilinear forms on $L_1[0,1]$, J. Math. Anal. Appl., to appear.
  • [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] V. Dimant and S. Dineen, Banach subspaces of spaces of holomorphic functions and related topics, preprint.
  • [11] V. Dimant and I. Zalduendo, Bases in spaces of multilinear forms over Banach spaces, J. Math. Anal. Appl. 200 (1996), 548-566.
  • [12] D. J. H. Garling, On symmetric sequence spaces, Proc. London Math. Soc. 16 (1966), 85-106.
  • [13] R. Gonzalo and J. A. Jaramillo, Compact polynomials between Banach spaces, Extracta Math. 8 (1993), 42-48.
  • [14] W. T. Gowers, Symmetric block bases of sequences with large average growth, Israel J. Math. 69 (1990), 129-151.
  • [15] P. Harmand, D. Werner and W. Werner, M-Ideals in Banach Spaces and Banach Algebras, Lecture Notes in Math. 1547, Springer, Berlin, 1993.
  • [16] H. Knaust, Orlicz sequence spaces of Banach-Saks type, Arch. Math. (Basel) 59 (1992), 562-565.
  • [17] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer, 1977.
  • [18] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer, 1979.
  • [19] S. Reisner, A factorization theorem in Banach lattices and its applications to Lorentz spaces, Ann. Inst. Fourier (Grenoble) 31 (1) (1981), 239-255.
  • [20] W. L. C. Sargent, Some sequence spaces related to the $l_p$ spaces, J. London Math. Soc. 35 (1960), 161-171.
  • [21] A. E. Tong, Diagonal submatrices of matrix maps, Pacific J. Math. 32 (1970), 551-559.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv127i2p99bwm
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