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A simple formula showing L¹ is a maximal overspace for two-dimensional real spaces

B. L. ChalmersF. T. Metcalf — 1992

Annales Polonici Mathematici

It follows easily from a result of Lindenstrauss that, for any real twodimensional subspace v of L¹, the relative projection constant λ(v;L¹) of v equals its (absolute) projection constant λ ( v ) = s u p X λ ( v ; X ) . The purpose of this paper is to recapture this result by exhibiting a simple formula for a subspace V contained in L ( ν ) and isometric to v and a projection P from C ⊕ V onto V such that P = P , where P₁ is a minimal projection from L¹(ν) onto v. Specifically, if P = i = 1 2 U i v i , then P = i = 1 2 u i V i , where d V i = 2 v i d ν and d U i = - 2 u i d ν .

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