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Operator Algebras with Unique Preduals
  Published:2011-03-10
 Printed: Sep 2011
Canadian Mathematical Bulletin
  • Kenneth R. Davidson,
    Pure Math. Dept., U. Waterloo, Waterloo, ON N2L--3G1
  • Alex Wright,
    Pure Math. Dept., U. Waterloo, Waterloo, ON N2L--3G1
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Abstract

We show that every free semigroup algebra has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak-$*$ closed unital operator algebra containing a weak-$*$ dense subalgebra of compact operators has a unique Banach space predual.
Keywords: unique predual, free semigroup algebra, CSL algebra unique predual, free semigroup algebra, CSL algebra
MSC Classifications: 47L50, 46B04, 47L35 show english descriptions Dual spaces of operator algebras
Isometric theory of Banach spaces
Nest algebras, CSL algebras 47L50 - Dual spaces of operator algebras
46B04 - Isometric theory of Banach spaces
47L35 - Nest algebras, CSL algebras
 
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