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Abstrakty
We give sufficient and necessary conditions for complex extreme points of the unit ball of Orlicz-Lorentz spaces, as well as we find criteria for the complex rotundity and uniform complex rotundity of these spaces. As an application we show that the set of norm-attaining operators is dense in the space of bounded linear operators from d* (w, 1) into d(w, 1), where d*(w, 1) is a predual of a complex Lorentz sequence space d[w, 1), if and only if w [is an element of] c0 \ L2.
Wydawca
Rocznik
Tom
Strony
19--38
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Division of Applied Mathematics, Korea Advanced Institute of Science and Technology, 373-1, Kusong-Dong, Yusong-Gu, Taejon, 305-701, Republic of Korea
autor
- Department of Mathematical Sciences, The University of Memphis Memphis, TN 38152, U.S.A.
autor
- Division of Applied Mathematics, Korea Advanced Institute of Science and Technology, 373-1, Kusong-Dong, Yusong-Gu, Taejon, 305-701, Republic of Korea
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] Z. Altshuler, Uniform convexity in Lorentz sequence spaces, ibid. 20 (1975), 260-274.
- [3] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, 1988.
- [4] E. Bishop and R.R. Phelps, A proof that every Banach space is subreexive, Bull. Amer. Math. Soc. 67 (1961), 97-98.
- [5] J. Cerdá, H. Hudzik, A. Kamińska and M. Mastyło, Geometric properties of symmetric spaces with applications to Orlicz-Lorentz spaces, Positivity 2 (1998), 311-337.
- [6] S. T. Chen, Geometry of Orlicz Spaces, Dissertationes Math. 356 (1996).
- [7] W. Davis, D. J. H. Garling and N. Tomczak-Jaegermann, The complex convexity of quasi-normed linear spaces, J. Funct. Anal. 55 (1984), 110-150.
- [8] J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge Univ. Press, 1995.
- [9] S. J. Dilworth, Complex convexity and the geometry of Banach spaces, Math. Proc. Cambridge Philos. Soc. 99 (1986), 495-506.
- [10] J. Globevnik, On complex strict and uniform convexity, Proc. Amer. Math. Soc. 47 (1975), 175-178.
- [11] W. T. Gowers, Symmetric block bases of sequences with large average growth, Israel J. Math. 69 (1990), 129-151.
- [12] I. Halperin, Uniform convexity in function spaces, Duke Math. J. 21 (1954), 195-204.
- [13] K. H. Han and H. G. Song, Extensions of polynomials on preduals of Lorentz sequence spaces, preprint, 2002.
- [14] M. Jiménez Sevilla and R. Payá, Norm-attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces, Studia Math. 127 (1998), 99-112.
- [15] A. Kamińska, Extreme points in Orlicz-Lorentz spaces, Arch. Math. (Basel) 55 (1990), 173-180.
- [16] -, Some remarks on Orlicz-Lorentz spaces, Math. Nachr. 147 (1990), 29-38.
- [17] -, Uniform convexity of generalized Lorentz spaces, Arch. Math. (Basel) 56 (1991), 181-188.
- [18] A. Kamińska and H. J. Lee, On uniqueness of extension of homogeneous polynomials, preprint, 2003.
- [19] A. Kamińska, P. K. Lin and H. Sun, Uniform normal structure of Orlicz-Lorentz spaces, in: Interaction Between Functional Analysis, Harmonic Analysis and Probability, Dekker, 1996, 229-238.
- [20] S. G. Kreĭn, Yu. I. Petunin and E. M. Semenov, Interpolation of Linear Operators, Transl. Math. Monogr. 54, Amer. Math. Soc., 1982.
- [21] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, 1983.
- [22] E. Thorp and R. Whitley, The strong maximum modulus theorem for analytic functions into a Banach space, Proc. Amer. Math. Soc. 18 (1967), 640-646.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0004-0003