### Subspaces of ${L}^{1}$ containing ${L}^{1}$

P. Enflo, T. Starbird (1979)

Studia Mathematica

Similarity:

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

P. Enflo, T. Starbird (1979)

Studia Mathematica

Similarity:

J. Arazy, J. Lindenstrauss (1975)

Compositio Mathematica

Similarity:

W. B. Johnson, E. Odell (1974)

Compositio Mathematica

Similarity:

C. Bessaga, A. Pełczyński (1958)

Studia Mathematica

Similarity:

Abad, Manuel, Monteiro, Luiz (1980)

Portugaliae mathematica

Similarity:

Ed Dubinsky, A. Pełczyński, H. Rosenthal (1972)

Studia Mathematica

Similarity:

C. Leránoz (1992)

Studia Mathematica

Similarity:

We prove that if 0 < p < 1 then a normalized unconditional basis of a complemented subspace of ${c}_{0}\left({l}_{p}\right)$ must be equivalent to a permutation of a subset of the canonical unit vector basis of ${c}_{0}\left({l}_{p}\right)$. In particular, ${c}_{0}\left({l}_{p}\right)$ has unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss, and Tzafriri have previously proved the same result for ${c}_{0}\left(l\u2081\right)$.

Alfred Andrew (1979)

Studia Mathematica

Similarity:

A. Pličko (1986)

Studia Mathematica

Similarity:

P. Casazza, N. Kalton (1999)

Studia Mathematica

Similarity:

We give counterexamples to a conjecture of Bourgain, Casazza, Lindenstrauss and Tzafriri that if X has a unique unconditional basis (up to permutation) then so does ${c}_{0}\left(X\right)$. We also give some positive results including a simpler proof that ${c}_{0}\left({\ell}_{1}\right)$ has a unique unconditional basis and a proof that ${c}_{0}\left({\ell}_{{p}_{n}}^{{N}_{n}}\right)$ has a unique unconditional basis when ${p}_{n}\uffec1$, ${N}_{n+1}\ge 2{N}_{n}$ and $({p}_{n}-{p}_{n+1})log{N}_{n}$ remains bounded.

P. Wojtaszczyk (1973)

Studia Mathematica

Similarity: