J. Aust. Math. Soc.  77 (2004), 365-369
The strong closure of Boolean algebras of projections in Banach spaces

J. Diestel
  Department of Mathematical Sciences
  Kent State University
  P.O. Box 5190
  Kent OH 44242-0001
  USA
  diestelj@aol.com
and
W. J. Ricker
  Math.-Geogr. Fakultät
  Katholische Universität
  Eichstätt-Ingolstadt
  D-85072 Eichstätt
  Germany
  werner.ricker@ku-eichstaett.de


Abstract
This note improves two previous results of the second author. They turn out to be special cases of our main theorem which states: A Banach space $X$ has the property that the strong closure of every abstractly $\sigma$-complete Boolean algebra of projections in $X$ is Bade complete if and only if $X$ does not contain a copy of the sequence space $\ell^\infty$.
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