Geodesic
A simple formula showing L¹ is a maximal overspace for two-dimensional real spaces
Annales Polonici Mathematici, Tome 56 (1991) no. 3, pp. 303-309.

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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 $λ(v) = sup_X λ(v;X)$. 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 $∥P_∞∥ = ∥P₁∥$, where P₁ is a minimal projection from L¹(ν) onto v. Specifically, if $P₁ = ∑_{i=1}^2 U_i ⊗ v_i$, then $P_∞ = ∑_{i=1}^2 u_i ⊗ V_i$, where $dV_i = 2v_i dν$ and $dU_i = -2u_i dν$.
DOI : 10.4064/ap-56-3-303-309
Keywords: maximal overspace, two-dimensional spaces

B. Chalmers 1 ; F. Metcalf 1

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B. Chalmers; F. Metcalf. A simple formula showing L¹ is a maximal overspace for two-dimensional real spaces. Annales Polonici Mathematici, Tome 56 (1991) no. 3, pp. 303-309. doi : 10.4064/ap-56-3-303-309. http://geodesic.mathdoc.fr/articles/10.4064/ap-56-3-303-309/

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