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Proceedings of the American Mathematical Society

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Relatively uniform Banach lattices

Author: Andrew Wirth
Journal: Proc. Amer. Math. Soc. 52 (1975), 178-180
MSC: Primary 46A40
MathSciNet review: 0374862
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Abstract: Sequential relative uniform and norm convergence agree in a Banach lattice, if and only if it is equivalent to an $M$ space.

References [Enhancements On Off] (What's this?)

  • Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
  • K. Knopp, Theory and application of infinite series, 2nd English ed., Blackie, London, 1951.
  • Solomon Leader, Sequential convergence in lattice groups, Problems in analysis (Sympos. dedicated to Salomon Bochner, Princeton Univ., Princeton, N.J., 1969) Princeton Univ. Press, Princeton, N.J., 1970, pp. 273–290. MR 0344842
  • A. C. Zaanen, Stability of order convergence and regularity in Riesz spaces, Studia Math. 31 (1968), 159–172. MR 240597, DOI

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Keywords: Banach lattice, relative uniform convergence, order convergence, <IMG WIDTH="27" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="$M$"> space, <IMG WIDTH="33" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${L^P}$"> space
Article copyright: © Copyright 1975 American Mathematical Society