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2010 | 8 | 2 | 346-356
Tytuł artykułu

Daugavet centers and direct sums of Banach spaces

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EN
Abstrakty
EN
A linear continuous nonzero operator G: X → Y is a Daugavet center if every rank-1 operator T: X → Y satisfies ||G + T|| = ||G|| + ||T||. We study the case when either X or Y is a sum X 1⊕F X 2 of two Banach spaces X 1 and X 2 by some two-dimensional Banach space F. We completely describe the class of those F such that for some spaces X 1 and X 2 there exists a Daugavet center acting from X 1⊕F X 2, and the class of those F such that for some pair of spaces X 1 and X 2 there is a Daugavet center acting into X 1⊕F X 2. We also present several examples of such Daugavet centers.
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
2
Strony
346-356
Opis fizyczny
Daty
wydano
2010-04-01
online
2010-04-14
Twórcy
Bibliografia
  • [1] Bilik D., Kadets V., Shvidkoy R., Werner D., Narrow operators and the Daugavet property for ultraproducts, Positivity, 2005, 9, 45–62 http://dx.doi.org/10.1007/s11117-003-9339-9
  • [2] Bourgain J., Rosenthal H.P., Martingales valued in certain subspaces of L 1, Israel J. Math., 1980, 37, 54–75 http://dx.doi.org/10.1007/BF02762868
  • [3] Bosenko T., Kadets V., Daugavet centers, Zh. Mat. Fiz. Anal. Geom., preprint available at http://arxiv.org/abs/0910.4503
  • [4] Daugavet I.K., On a property of completely continuous operators in the space C, Uspekhi Mat. Nauk, 1963, 18, 157–158 (in Russian)
  • [5] Kadets V.M., Shepelska V., Werner D., Quotients of Banach spaces with the Daugavet property, Bull. Pol. Acad. Sci. Math., 2008, 56, 131–147 http://dx.doi.org/10.4064/ba56-2-5
  • [6] Kadets V.M., Shvidkoy R.V., Sirotkin G.G., Werner D., Banach spaces with the Daugavet property, Trans. Amer. Math. Soc., 2000, 352, 855–873 http://dx.doi.org/10.1090/S0002-9947-99-02377-6
  • [7] Kadets V.M., Werner D., A Banach space with the Schur and the Daugavet property, Proc. Amer. Math. Soc., 2004, 132, 1765–1773 http://dx.doi.org/10.1090/S0002-9939-03-07278-2
  • [8] Lindenstrauss J., Tzafriri L., Classical Banach Spaces II: Function spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1979
  • [9] Lozanovskii G.Ya., On almost integral operators in KB-spaces, Vestnik Leningrad Univ. Mat. Mekh. Astr., 1966, 21, 35–44 (in Russian)
  • [10] Popov M.M., Daugavet type inequalities for narrow operators in the space L 1, Mat. Stud., 2003, 20, 75–84
  • [11] Shvidkoy R.V., Geometric aspects of the Daugavet property, J. Funct. Anal., 2000, 176, 198–212 http://dx.doi.org/10.1006/jfan.2000.3626
  • [12] Talagrand M., The three-space problem for L 1, J. Amer. Math. Soc., 1990, 3, 9–29 http://dx.doi.org/10.2307/1990983
  • [13] Werner D., Recent progress on the Daugavet property, Irish Math. Soc. Bull., 2001, 46, 77–97
  • [14] Werner D., The Daugavet equation for operators on function spaces, J. Funct. Anal., 1997, 143, 117–128 http://dx.doi.org/10.1006/jfan.1996.2979
  • [15] Wojtaszczyk P., Some remarks on the Daugavet equation, Proc. Amer. Math. Soc., 1992, 115, 1047–1052 http://dx.doi.org/10.2307/2159353
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0015-6
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