WEAK\star- INVARIANTLY COMPLEMENTED SUBSPACES OF L^{\infty}(1/\omega) AND IDEALS OF L^{1}(\omega) WITH A BOUNDED APPROXIMATE IDENTITY

Authors: Z. ARGÜN, C. TONYALI

Abstract: For a locally compact group G let L^{1}(\omega) be the weighted group algebra and let X be a weak \star-closed translation invariant subspace of L^{\infty} (1/\omega). In this paper for a certain class of functions we show that the following conditions are equivalent: (i) X is topological invariantly complemented in L^{\infty}(1/\omega); (ii) X is invariantly complemented in L^{\infty}(1/\omega); (iii) The left ideal X_{\perp} has a bounded right approximate identity.

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