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The Order Properties of r-compact Operators on Banach Lattices 被引量：2

The Order Properties of r-compact Operators on Banach Lattices
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摘要 We present here that F（E,F）, the space of all r-compact operators from E into F, is a generalised sublattice of L^r（E, F） for arbitary Banach lattices E and F, and that the characterization of the regular norm on F（E, F） is order continuous. Some conditions for F（E, F） to be a KB-space or a band in .L（E, F） are also provided. We present here that F（E,F）, the space of all r-compact operators from E into F, is a generalised sublattice of L^r（E, F） for arbitary Banach lattices E and F, and that the characterization of the regular norm on F（E, F） is order continuous. Some conditions for F（E, F） to be a KB-space or a band in .L（E, F） are also provided.
作者 Zi Li CHEN A. W. WICKSTEAD
机构地区 Department of Mathematics Department of Pure Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第3期457-466,共10页 数学学报（英文版）
关键词 Banach lattice KB-SPACE regular norm order continuous norm r-compact operator Banach lattice, KB-space, regular norm, order continuous norm, r-compact operator
分类号 O177 [理学—基础数学]
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参考文献15

  • 1Meyer-Nieberg, P.: Banach lattices, Springer-Verlag, Berlin, Heidelberg, New York, 1991
  • 2Abramovich, Y. A., Wickstead, A. W.: Solutions of several problems in the theory of compact positive operators. Proc. Amer. Math. Soc., 123, 3021-3026 (1995)
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  • 4Chen, Z. L., Wickstead, A. W.: Some applications of Rademacher sequences in Banach lattices. Positivity,2, 171-191 (1998)
  • 5Arendt, W.: On the o-spectrum of regular operators and the spectrum of measures. Math. Z., 178, 271-287(1981)
  • 6Arendt, W., Sourour, A. R.: Ideals of the regular operators on L^2. Proc. Amer. Math. Soc., 88, 93-96(1983)
  • 7Arendt, W., Sourour, A. R.: Perturbation of regular operators and the order essential spectrum. Indag.Math., 89, 109-122 (1986)
  • 8Wickstead, A. W.: Positive compact operators on Banach lattices: Some loose end. Positivity, 4, 313 325(2000)
  • 9Wickstead, A. W: Airspaces and AM-spaces of operators. Positivity, 4, 303-311 (2000)
  • 10Abramovich, Y. A., Wickstead, A. W.: Recent results on the order structure of compact operators. Irish Math. Soc. Bulletin, 32, 32-45 (1994)

引证文献2

Acta Mathematica Sinica,English Series
2007年 第3期

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