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1-Complemented Subspaces of Spaces With 1-Unconditional Bases

Published online by Cambridge University Press:  20 November 2018

Beata Randrianantoanina
Beata Randrianantoanina*
Affiliation:
Department of Mathematics 123 Bachelor Hall Miami University Oxford, OH 45056-1641, USA
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Abstract

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We prove that if X is a complex strictly monotone sequence space with 1-unconditional basis, Y ⊆ X has no bands isometric to ℓ22 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.

Keywords

46B2046B4541A65
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 6 , 01 December 1997 , pp. 1242 - 1264
Copyright
Copyright © Canadian Mathematical Society 1997

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