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2009 | 7 | 4 | 683-693
Tytuł artykułu

On order structure and operators in L ∞(μ)

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is known that there is a continuous linear functional on L ∞ which is not narrow. On the other hand, every order-to-norm continuous AM-compact operator from L ∞(μ) to a Banach space is narrow. We study order-to-norm continuous operators acting from L ∞(μ) with a finite atomless measure μ to a Banach space. One of our main results asserts that every order-to-norm continuous operator from L ∞(μ) to c 0(Γ) is narrow while not every such an operator is AM-compact.
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
4
Strony
683-693
Opis fizyczny
Daty
wydano
2009-12-01
online
2009-10-31
Twórcy
  • Department of Mathematics, Zaporizhzhya National University, Zaporizhzhya, Ukraine, yudp@mail.ru
  • Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Granada, Spain, mmartins@ugr.es
autor
  • Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Granada, Spain, jmeri@ugr.es
  • Department of Mathematics, Chernivtsi National University, Chernivtsi, Ukraine, mathan@ukr.net
Bibliografia
  • [1] Albiac F., Kalton N., Topics in Banach Space Theory, Graduate Texts in Mathematics 233, Springer, New York, 2006
  • [2] Aliprantis CD., Burkinshaw O., Positive Operators, Springer, Dordrecht, 2006
  • [3] Benyamini Y., Lin P.-K., An operator on L p without best compact approximation, Israel J. Math., 1985, 51, 298–304 http://dx.doi.org/10.1007/BF02764722[Crossref]
  • [4] Flores J., Ruiz C, Domination by positive narrow operators, Positivity, 2003, 7, 303–321 http://dx.doi.org/10.1023/A:1026211909760[Crossref]
  • [5] Jech Th., Set Theory, Springer, Berlin, 2003
  • [6] Kadets V, Martín M., Merí J., Shepelska V, Lushness, numerical index one and duality, J. Math. Anal. Appl., 2009, 357, 15–24 http://dx.doi.org/10.1016/j.jmaa.2009.03.055[Crossref]
  • [7] Kadets V.M., Popov M.M., On the Liapunov convexity theorem with applications to sign-embeddings, Ukr. Mat. Zh., 1992, 44(9), 1192–1200 http://dx.doi.org/10.1007/BF01058369[Crossref]
  • [8] Kadets V.M., Popov M.M., The Daugavet property for narrow operators in rich subspaces of the spaces C[0,1] and L 1[0,1], Algebra i Analiz, 1996, 8, 43–62 (in Russian), English translation: St. Petersburg Math. J., 1997, 8, 571–584
  • [9] Krasikova I.V., A note on narrow operators in L ∞, Math. Stud., 2009, 31(1), 102–106
  • [10] Lindenstrauss J., Pełczyński A., Absolutely summing operators in ℒp-spaces and their applications, Studia Math, 1968, 29, 275–326
  • [11] Lindenstrauss J., Tzafriri L., Classical Banach Spaces, Vol. 1, Sequence spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1977
  • [12] Lindenstrauss J., Tzafriri L., Classical Banach Spaces, Vol. 2, Function spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1979
  • [13] Maslyuchenko O.V, Mykhaylyuk V.V., Popov M.M., A lattice approach to narrow operators, Positivity, 2009, 13, 459–495 http://dx.doi.org/10.1007/s11117-008-2193-z[Crossref]
  • [14] Plichko A.M., Popov M.M., Symmetric function spaces on atomless probability spaces, Dissertationes Math., 1990, 306, 1–85
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0047-y
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