Finite-dimensional left ideals in the duals of introverted spaces

Filali, M.; Monfared, M.

doi:10.1090/S0002-9939-2011-10784-6

Finite-dimensional left ideals in the duals of introverted spaces
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by M. Filali and M. Sangani Monfared PDF

Proc. Amer. Math. Soc. 139 (2011), 3645-3656 Request permission

Abstract:

We use representations of a Banach algebra $A$ to completely characterize all finite-dimensional left ideals in the dual of introverted subspaces of $A^*$ and in particular in the double dual $A^{**}$. We give sufficient conditions under which such ideals always exist and are direct sums of one-dimensional left ideals.

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