Positive Schur properties in spaces of regular operators

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• 作者：Pedro Tradacete
• 关键词：Banach lattice ; Positive Schur property ; Positive Grothendieck property ; Spaces of regular operators ; Fremlin tensor product ; 46B42 ; 46A32 ; 47B65
• 刊名：Positivity
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：19
• 期：2
• 页码：305-316
• 全文大小：433 KB
• 参考文献：1.Aliprantis, C.D., Burkinshaw, O.: Positive Operators. Springer, New York (2006)
  2.Aqzzouz, B., Elbour, A., Wickstead, A.W.: Positive almost Dunford–Pettis operators and their duality. Positivity 15, 185-97 (2011)MATH MathSciNet View Article
  3.Bu, Q., Buskes, G., Popov, A.I., Tcaciuc, A., Troitsky, V.G.: The 2-concavification of a Banach lattice equals the diagonal of the Fremlin tensor square. Positivity 17(2), 283-98 (2013)MATH MathSciNet View Article
  4.Diestel, J.: A survey of results related to the Dunford–Pettis property. In: Proceedings of the Conference on Integration, Topology, and Geometry in Linear Spaces (Univ. North Carolina, Chapel Hill, N.C., 1979), pp. 15-0, Contemp. Math., 2, Am. Math. Soc. (1980)
  5.Flores, J., Hernández, F.L., Spinu, E., Tradacete, P., Troitsky, V.G.: Disjointly homogeneous Banach lattices: duality and complementation. J. Funct. Anal. 266, 5858-885 (2014)MATH MathSciNet View Article
  6.Fremlin, D.H.: Tensor products of Archimedean vector lattices. Am. J. Math. 94, 777-98 (1972)MATH MathSciNet View Article
  7.Fremlin, D.H.: Tensor products of Banach lattices. Math. Ann. 211, 87-06 (1974)MATH MathSciNet View Article
  8.Ji, D., Craddock, M., Bu, Q.: Reflexivity and the Grothendieck property for positive tensor products of Banach lattices. I. Positivity 14(1), 59-8 (2010)MATH MathSciNet View Article
  9.Labuschagne, C.C.A.: Riesz reasonable cross norms on tensor products of Banach lattices. Quaest. Math. 27(3), 243-66 (2004)MATH MathSciNet View Article
  10.Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces. Springer, New York (1979)MATH View Article
  11.Meyer-Nieberg, P.: Banach Lattices. Springer, New York (1991)
  12.Troitsky, V.G., Zabeti, O.: Fremlin tensor products of concavifications of Banach lattices. Positivity 18(1), 191-00 (2014)MATH MathSciNet View Article
  13.Wickstead, A.W.: AL-spaces and AM-spaces of operators. Positivity and its applications (Ankara, 1998). Positivity 4(3), 303-11 (2000)MATH MathSciNet View Article
  14.Wnuk, W.: Some remarks on the positive Schur property in spaces of operators. Funct. Approx. Comment. Math. 21, 65-8 (1992)MATH MathSciNet
  15.Wnuk, W.: Banach lattices with properties of the Schur type—a survey. Conferenze del Seminario di Matematica dell’Università di Bari 249, 1-4 (1993)MathSciNet
  16.Wnuk, W.: On the dual positive Schur property in Banach lattices. Positivity 17(3), 759-73 (2013)MATH MathSciNet View Article
  
• 作者单位：Pedro Tradacete (1)
  
  1. Mathematics Department, Universidad Carlos III de Madrid, 28911?, Leganés (Madrid), Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Fourier Analysis
  Operator Theory
  Potential Theory
  Calculus of Variations and Optimal Control
  Econometrics
  
• 出版者：Birkh盲user Basel
• ISSN：1572-9281

文摘

Properties of Schur type for Banach lattices of regular operators and tensor products are analyzed. It is shown that the dual positive Schur property behaves well with respect to Fremlin’s projective tensor product, which allows us to construct new examples of spaces with this property. Similar results concerning the positive Grothendieck property are also presented.