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A note on strict K-monotonicity of some symmetric function spaces

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We discuss some sufficient and necessary conditions for strict K-monotonicity of some important concrete symmetric spaces. The criterion for strict monotonicity of the Lorentz space Γp,w with 0 < p < ∞ is given.
Rocznik
Strony
211--222
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
  • Institute of Mathematics, Poznan University of Technology, Piotrowo 3A, 60-965 Poznan
autor
  • Institute of Mathematics, Poznan University of Technology, Piotrowo 3A, 60-965 Poznan
  • Institute of Mathematics, Poznan University of Technology, Piotrowo 3A, 60-965 Poznan
Bibliografia
  • [1] C. Bennett and R. Sharpley, Interpolation of operators, Pure and Applied Mathematics Series 129, Academic Press Inc.,1988.
  • [2] A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113–190.
  • [3] V. I. Chilin, P. G. Dodds, A. A. Sedaev, and F. A. Sukochev, Characterizations of Kadec-Klee properties in symmetric spaces of measurable functions, Trans. Amer. Math. Soc. 348,12 (1996), 4895-4918.
  • [4] M. Ciesielski, A. Kaminska and R. Płuciennik, Gâteaux derivatives and their applications to approximation in Lorentz spaces Γp,w, Math. Nachr. 282,9 (2009), 1242-1264.
  • [5] M. Ciesielski, A. Kaminska, P. Kolwicz and R. Płuciennik, Monotonicity and rotundity of Lorentz spaces Γp,w, Nonlinear Analysis 75 (2012), 2713-2723.
  • [6] M. Ciesielski, P. Kolwicz and A. Panfil Local monotonicity structure of Lorentz spaces Γp,w, J. Math. Anal. Appl. 409 (2014), 649-642.
  • [7] I. Dobrakov, On submeasures I, Diss. Math. 62 (1974), 1–35.
  • [8] H. Hudzik and A. Kaminska, Monotonicity properties of Lorentz spaces, Proc. Amer. Math. Soc. 123,9, (1995), 2715-2721.
  • [9] H. Hudzik, A. Kaminska and M. Mastyło, Geometric properties of some Calderón-Lozanovski˘I spaces and Orlicz-Lorentz spaces, Houston J. Math. 22, (1996), 639-663.
  • [10] H. Hudzik, A. Kaminska and M. Mastyło, Monotonicity and rotundity properties in Banach lattices, Rocky Mountain J. Math. 30.3 (2000), 933-949.
  • [11] H. Hudzik, A. Kaminska and M. Mastyło, Geometric properties of some Calderón-Lozanovski˘ı spaces and Orlicz-Lorentz spaces, Houston J. Math. 22 (1996), 639-663.
  • [12] H. Hudzik, A. Kaminska and M. Mastyło, On geometric properties of Orlicz-Lorentz spaces, Canad. Math. Bull. 40,3 (1997), 316-329.
  • [13] A. Kaminska, Some remarks on Orlicz-Lorentz spaces, Math. Nachr. 147 (1990), 29-38.
  • [14] A. Kaminska and L. Maligranda, Order convexity and concavity of Lorentz spaces Λp, w, 0 < p < ∞, Studia Math. 160,3 (2004), 267-286.
  • [15] A. Kaminska and L. Maligranda, On Lorentz spaces Γp,w, Israel J. Math. 140 (2004), 285-318.
  • [16] A. Kaminska and A.M. Parrish, Note on extreme points in Marcinkiewicz function spaces, Banach J. Math. Anal. 4,1 (2010), 1-12.
  • [17] L. V. Kantorovich and G. P. Akilov, Functional analysis, Nauka (Moscow, 1984) (in Russian).
  • [18] P. Kolwicz, Rotundity properties in Calderón-Lozanovski˘ı spaces, Houston J. Math. 31,3 (2005), 883-912.
  • [19] P. Kolwicz, K. Lesnik and L. Maligranda, Pointwise multipliers of Calderón-Lozanovski˘I spaces, Math. Nachr. 286,8-9 (2013), 876-907.
  • [20] P. Kolwicz, K. Lesnik and L. Maligranda, Pointwise products of some Banach function spaces and factorization, J. Funct. Anal. 266,2 (2014), 616-659.
  • [21] S. G. Krein, Yu. I. Petunin and E. M. Semenov, Interpolation of linear operators, Nauka, Moscow, 1978 (in Russian).
  • [22] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. II. Function spaces, Springer-Verlag, Berlin-New York, 1979.
  • [23] G. G. Lorentz, On the theory of spaces Λ, Pacific J. Math. 1, (1951) 411-429.
  • [24] E. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96,2 (1990), 145-158.
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  • [26] W. Wnuk, Banach lattices with order continuous norms, Polish Scientific Publisher PWN, Warszawa 1999.
Typ dokumentu
Bibliografia
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