Unconditional bases for complemented subspaces of Tsirelson's space

1989 ◽  
pp. 82-94
Author(s):  
Peter G. Casazza ◽  
Thaddeus J. Shura
Keyword(s):  
Complemented Subspaces ◽  
Unconditional Bases

scholarly journals 1-Complemented Subspaces of Spaces With 1-Unconditional Bases

1997 ◽  
Vol 49 (6) ◽  
pp. 1242-1264 ◽  
Author(s):  
Beata Randrianantoanina
Keyword(s):  
Sequence Space ◽  
Lorentz Space ◽  
Linear Span ◽  
Full Description ◽  
Monotone Sequence ◽  
Closed Linear Span ◽  
Complex Spaces ◽  
Complemented Subspaces ◽  
Unconditional Bases ◽  
Constant Coefficients

AbstractWe 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.

On complemented subspaces of non-Archimedean Köthe spaces

2019 ◽  
Vol 470 (1) ◽  
pp. 401-412
Author(s):  
Wiesław Śliwa ◽  
Agnieszka Ziemkowska
Keyword(s):  
Complemented Subspaces ◽  
Köthe Spaces
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