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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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

1 
@article{10_4064_ap_56_3_303_309,
     author = {B. Chalmers and F. Metcalf},
     title = {A simple formula showing {L{\textonesuperior}} is a maximal overspace for two-dimensional real spaces},
     journal = {Annales Polonici Mathematici},
     pages = {303--309},
     year = {1991},
     volume = {56},
     number = {3},
     doi = {10.4064/ap-56-3-303-309},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-56-3-303-309/}
}
TY  - JOUR
AU  - B. Chalmers
AU  - F. Metcalf
TI  - A simple formula showing L¹ is a maximal overspace for two-dimensional real spaces
JO  - Annales Polonici Mathematici
PY  - 1991
SP  - 303
EP  - 309
VL  - 56
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap-56-3-303-309/
DO  - 10.4064/ap-56-3-303-309
LA  - en
ID  - 10_4064_ap_56_3_303_309
ER  - 
%0 Journal Article
%A B. Chalmers
%A F. Metcalf
%T A simple formula showing L¹ is a maximal overspace for two-dimensional real spaces
%J Annales Polonici Mathematici
%D 1991
%P 303-309
%V 56
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/ap-56-3-303-309/
%R 10.4064/ap-56-3-303-309
%G en
%F 10_4064_ap_56_3_303_309
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

Cité par Sources :