Marek Wisła

Extreme Points and Strong U-Points in Musielak-Orlicz Sequence Spaces Equipped with the Orlicz Norm

We give some criteria for extreme points and strong U-points in Musielak{ Orlicz sequence spaces equipped with the Orlicz norm. It follows from these results that the notion of the strong U-point is essentially stronger than the notion of the extreme point in these spaces. Keywords. Musielak{Orlicz sequence space, extreme point, strong U-point, Orlicz norm. Mathematics Subject Classiflcation (2000). Primary 46B20, 46E30, secondary 46A45

Monotonicity Properties of Banach Lattices and Their Applications – a Survey

This is a survey of the most important results from the wide literature concerning monotonicity properties of Banach lattices and their applications.

Function Spaces and Applications

Function spaces and its various applications are subjects of investigation in many research centers and we are glad that this special issue has received the remarkable attention by researchers in these areas. We have received papers from wide range of topics of function spaces such as interpolation methods for stochastic processes spaces, vector optimization problems in Banach spaces, Marcinkiewicz integral operator in Morrey spaces, Hardy’s operator in the variable exponent Lebesgue spaces, and differential equations of weakly parabolic type in Banach spaces. A number of papers are devoted to investigating different kinds of problems in Hardy spaces or Hardy subspaces, for example, Calderon-Zygumnd singular integral operators in Hardy spaces, weighted Hardy spaces related to the Schrodinger operator, and composition operator in hyperbolic Bloch-type spaces. Geometric problems such as modulus of convexity in some Banach sequence spaces, p-uniform convexity, and quniform smoothness in C spaces are also covered by this issue.