Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups

author

  • B. Mohammadzadeh Department of Mathematics, Faculty of Sciences, Babol University of Technology, Babol, Mazandaran, Islamic Republic of Iran
Abstract:

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenable if and only if every complemented weak*-closed left translation invariant subspace of   is invariantly  complemented in .

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Journal title

volume 25  issue 1

pages  51- 55

publication date 2014-03-01

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