Given two Banach function spaces X and Y related to a measure μ, the Y-dual space XY of X
is defined as the space of the multipliers from X to Y. The space XY is a generalization of the …

First, we present some simple (and easily verifiable) necessary conditions and sufficient
conditions for boundedness of the multiplication operator M_u M u and composition operator …

[EN] The lattice properties of the Banach lattices Lp (m) and Lpw (m) of p-integrable real-
valued functions and weakly p-integrable real-valued functions with respect to a vector …

Let ν be a countably additive vector measure defined on the Borel subsets of a compact
Hausdorff abelian group G. In this paper we define and study a vector valued Fourier …

Let m be a countably additive vector measure with values in a real Banach space X, and let
L1 (m) and Lw (m) be the spaces of functions which are, correspondingly, integrable and …

We study the equivalence between the Orlicz and Luxemburg (quasi-) norms in the context
of the generalized Orlicz spaces associated to an N-function Φ and a (quasi-) Banach …

In this paper, we discuss and characterize the boundedness, compactness and closed
range of the multiplication operator. Moreover, we obtain some new results about necessary …

Given three Banach spaces X, Y and Z and a bounded bilinear map B: X× Y→ Z, a
sequence [Formula: see text] is called B-absolutely summable if∑ n= 1∞‖ B (xn, y)‖ Z is …

Compactness of Multiplication Operators on Spaces of Integrable Functions with Respect to a
Vector Measure Page 1 Operator Theory: Advances and Applications, Vol. 201, 109–113 c© …

Compactness type properties for operators acting in Banach function spaces are not always
preserved when the operator is extended to a bigger space. Moreover, it is known that there …