Geodesic
1-Complemented Subspaces of Spaces With 1-Unconditional Bases
Canadian journal of mathematics, Tome 49 (1997) no. 6, pp. 1242-1264

Voir la notice de l'article provenant de la source Cambridge University Press

We prove that if X is a complex strictly monotone sequence space with 1-unconditional basis, Y ⊆ X has no bands isometric to l2 2 and Y is the range of norm-one projection from X, then Y is a closed linear span a family of mutually disjoint vectors in X.We completely characterize 1-complemented subspaces and norm-one projections in complex spaces lp(lq) for 1 ≤ p,q > ∞.Finally we give a full description of the subspaces that are spanned by a family of disjointly supported vectors and which are 1-complemented in (real or complex) Orlicz or Lorentz sequence spaces. In particular if an Orlicz or Lorentz space X is not isomorphic to lp for some 1 ≤ p,q > ∞ then the only subspaces of X which are 1-complemented and disjointly supported are the closed linear spans of block bases with constant coefficients.
DOI : 10.4153/CJM-1997-061-2
Mots-clés : 46B20, 46B45, 41A65 
Randrianantoanina, Beata. 1-Complemented Subspaces of Spaces With 1-Unconditional Bases. Canadian journal of mathematics, Tome 49 (1997) no. 6, pp. 1242-1264. doi: 10.4153/CJM-1997-061-2
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