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2000 | 142 | 3 | 269-280
Tytuł artykułu

Numerical index of vector-valued function spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that the numerical index of a $c_0$-, $l_1$-, or $l_∞$-sum of Banach spaces is the infimum of the numerical indices of the summands. Moreover, we prove that the spaces C(K,X) and $L_1(μ,X)$ (K any compact Hausdorff space, μ any positive measure) have the same numerical index as the Banach space X. We also observe that these spaces have the so-called Daugavet property whenever X has the Daugavet property.
Słowa kluczowe
Czasopismo
Rocznik
Tom
142
Numer
3
Strony
269-280
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-10-18
poprawiono
2000-06-19
Twórcy
  • Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
autor
  • Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Bibliografia
  • [1] Y. A. Abramovich, New classes of spaces on which compact operators satisfy the Daugavet equation, J. Operator Theory 25 (1991), 331-345.
  • [2] Y. A. Abramovich, C. D. Aliprantis and O. Burkinshaw, The Daugavet equation in uniformly convex Banach spaces, J. Funct. Anal. 97 (1991), 215-230.
  • [3] C. Aparicio, F. Oca na, R. Payá and A. Rodríguez, A non-smooth extension of Fréchet differentiability of the norm with applications to numerical ranges, Glasgow Math. J. 28 (1986), 121-137.
  • [4] H. F. Bohnenblust and S. Karlin, Geometrical properties of the unit sphere in Banach algebras, Ann. of Math. 62 (1955), 217-229.
  • [5] F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Math. Soc. Lecture Note Ser. 2, Cambridge Univ. Press, 1971.
  • [6] F. F. Bonsall and J. Duncan, Numerical Ranges II, London Math. Soc. Lecture Note Ser. 10, Cambridge Univ. Press, 1973.
  • [7] I. K. Daugavet, A property of completely continuous operators in the space C, Uspekhi Mat. Nauk 18 (1963), no. 5, 157-158 (in Russian).
  • [8] J. Diestel and J. J. Uhl, Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, 1977.
  • [9] J. Duncan, C. M. McGregor, J. D. Pryce and A. J. White, The numerical index of a normed space, J. London Math. Soc. (2) 2 (1970), 481-488.
  • [10] B. W. Glickfeld, On an inequality of Banach algebra geometry and semi-inner-product space theory, Illinois J. Math. 14 (1970), 76-81.
  • [11] K. E. Gustafson and D. K. M. Rao, Numerical Range. The Field of Values of Linear Operators and Matrices, Springer, New York, 1997.
  • [12] V. M. Kadets, R. V. Shvidkoy, G. G. Sirotkin et D. Werner, Espaces de Banach ayant la propriété de Daugavet, C. R. Acad. Sci. Paris Sér. I 325 (1997), 1291-1294.
  • [13] V. M. Kadets, R. V. Shvidkoy, G. G. Sirotkin et D. Werner, Banach spaces with the Daugavet property, Trans. Amer. Math. Soc. 352 (2000), 855-873.
  • [14] Å. Lima, On extreme operators on finite-dimensional Banach spaces whose unit balls are polytopes, Ark. Mat. 19 (1981), 97-116.
  • [15] G. López, M. Martín and R. Payá, Real Banach spaces with numerical index 1, Bull. London Math. Soc. 31 (1999), 207-212.
  • [16] G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961), 29-43.
  • [17] C. M. McGregor, Finite dimensional normed linear spaces with numerical index 1, J. London Math. Soc. (2) 3 (1971), 717-721.
  • [18] D. Werner, The Daugavet equation for operators on function spaces, J. Funct. Anal. 143 (1997), 117-128.
  • [19] P. Wojtaszczyk, Some remarks on the Daugavet equation, Proc. Amer. Math. Soc. 115 (1992), 1047-1052.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv142i3p269bwm
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