Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Tauberian operators on $L_1(μ)$ spaces

100%

Gonzalez M., Martínez-Abejón A.

Studia Mathematica

1997

tom 125

nr 3

289-303

We characterize tauberian operators $T:L_1(μ) → Y$ in terms of the images of disjoint sequences and in terms of the image of the dyadic tree in $L_1[0,1]$. As applications, we show that the class of tauberian operators is stable under small norm perturbations and that its perturbation class coincides with the class of all weakly precompact operators. Moreover, we prove that the second conjugate of a tauberian operator $T:L_1(μ) → Y$ is also tauberian, and the induced operator $T̃: L_1(μ)**/L_1(μ) → Y**/Y$ is an isomorphism into. Also, we show that $L_1(μ)$ embeds isomorphically into the quotient of $L_1(μ)$ by any of its reflexive subspaces.

Local dual spaces of a Banach space

100%

González M., Martínez-Abejón A.

Studia Mathematica

2001

tom 147

nr 2

155-168

We study the local dual spaces of a Banach space X, which can be described as the subspaces of X* that have the properties that the principle of local reflexivity attributes to X as a subspace of X**. We give several characterizations of local dual spaces, which allow us to show many examples. Moreover, every separable space X has a separable local dual Z, and we can choose Z with the metric approximation property if X has it. We also show that a separable space containing no copies of ℓ₁ admits a smallest local dual.

Ograniczanie wyników

2 Studia Mathematica

2 Martínez-Abejón A.

1 Gonzalez M.

1 González M.

1 2001

1 1997

Wyniki wyszukiwania

Tauberian operators on $L_1(μ)$ spaces

Local dual spaces of a Banach space