Wyniki wyszukiwania

1

Uniqueness of unconditional basis of $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$, 0 < p < 1

100%

Albiac F., Leránoz C.

Studia Mathematica

|

2002

|

tom 150

|

nr 1

35-52

EN

We prove that the quasi-Banach spaces $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$ (0 < p < 1) have a unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss and Tzafriri have previously proved that the same is true for the respective Banach envelopes $ℓ₁(c₀)$ and ℓ₁(ℓ₂). They used duality techniques which are not available in the non-locally convex case.

2

On a problem posed by M. M. Popov

100%

Albiac F., Ansorena J.

Studia Mathematica

|

2012

|

tom 211

|

nr 3

247-258

EN

We show that if X is a non-locally convex quasi-Banach space with a rich dual, there exists a continuous function f: [0,1] → X failing to have a primitive. This answers a twenty year-old question raised by M. Popov in this journal.

3

Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces

71%

Albiac F., Ansorena J., Garrigós G., Hernández E., Raja M.

Studia Mathematica

|

2015

|

tom 227

|

nr 2

133-140

EN

We show that in a super-reflexive Banach space, the conditionality constants $k_{N}(ℬ)$ of a quasi-greedy basis ℬ grow at most like $O((log N)^{1-ε})$ for some 0 < ε < 1. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in $L_{p}$ for 1 < p < ∞. We also give an example of a quasi-greedy basis ℬ in a reflexive Banach space with $k_{N}(ℬ) ≈ log N$.

Ograniczanie wyników

3 Studia Mathematica

3 Albiac F.

2 Ansorena J.

1 Garrigós G.

1 Hernández E.

1 Leránoz C.

1 Raja M.

1 2015

1 2012

1 2002

Uniqueness of unconditional basis of $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$, 0 < p < 1

On a problem posed by M. M. Popov

Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces