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1.
Let φ be an Orlicz function that has a complementary function φ* and let ℓφ be an Orlicz sequence space. We prove two results in this paper. Result 1:
, the Fremlin projective tensor product of ℓφ with a Banach lattice X, has the Radon-Nikodym property if and only if both ℓφ and X have the Radon-Nikodym property. Result 2:
, the Wittstock injective tensor product of ℓφ with a Banach lattice X, has the Radon-Nikodym property if and only if both ℓφ and X have the Radon-Nikodym property and each positive continuous linear operator from hφ* to X is compact.
We dedicate this paper to the memory of H. H. Schaefer
The first-named author gratefully acknowledges support from the Faculty Research Program of the University of Mississippi
in summer 2004. 相似文献
2.
In this paper, the authors consider the boundedness of generalized higher commutator of Marcinkiewicz integral μΩ^b, multilinear Marcinkiewicz integral μΩ^A and its variation μΩ^A on Herz-type Hardy spaces, here Ω is homogeneous of degree zero and satisfies a class of L^s-Dini condition. And as a special case, they also get the boundedness of commutators of Marcinkiewicz integrals on Herz-type Hardy spaces. 相似文献
3.
Let A and B be Banach function algebras on compact Hausdorff spaces X and Y and let ‖.‖
X
and ‖.‖
Y
denote the supremum norms on X and Y, respectively. We first establish a result concerning a surjective map T between particular subsets of the uniform closures of A and B, preserving multiplicatively the norm, i.e. ‖Tf Tg‖
Y
= ‖fg‖
X
, for certain elements f and g in the domain. Then we show that if α ∈ ℂ {0} and T: A → B is a surjective, not necessarily linear, map satisfying ‖fg + α‖
X
= ‖Tf Tg + α‖
Y
, f,g ∈ A, then T is injective and there exist a homeomorphism φ: c(B) → c(A) between the Choquet boundaries of B and A, an invertible element η ∈ B with η(Y) ⊆ {1, −1} and a clopen subset K of c(B) such that for each f ∈ A,
$
Tf\left( y \right) = \left\{ \begin{gathered}
\eta \left( y \right)f\left( {\phi \left( y \right)} \right) y \in K, \hfill \\
- \frac{\alpha }
{{\left| \alpha \right|}}\eta \left( y \right)\overline {f\left( {\phi \left( y \right)} \right)} y \in c\left( B \right)\backslash K \hfill \\
\end{gathered} \right.
$
Tf\left( y \right) = \left\{ \begin{gathered}
\eta \left( y \right)f\left( {\phi \left( y \right)} \right) y \in K, \hfill \\
- \frac{\alpha }
{{\left| \alpha \right|}}\eta \left( y \right)\overline {f\left( {\phi \left( y \right)} \right)} y \in c\left( B \right)\backslash K \hfill \\
\end{gathered} \right.
相似文献
4.
Let U(λ, μ) denote the class of all normalized analytic functions f in the unit disk |z| < 1 satisfying the condition
|