Extreme points in Orlicz spaces equipped with s$s$‐norms and closedness

Extreme Points and Rotundity in Musielak-Orlicz-Bochner Function Spaces Endowed with Orlicz Norm

and Applied Analysis 3 Put LM X { u ∈ XT : ρM λu < ∞ for some λ > 0 } . 1.5 Then the Musielak-Orlicz-Bochner function space ‖u‖ inf k>0 1 k [ 1 ρM ku ] 1.6 is Banach space. If X R, LM R is said to be Musielak-Orlicz function space. Set K u { k > 0 : 1 k ( 1 ρM ku ) ‖u‖ } . 1.7 In particular, the set K u can be nonempty. To show that, we give a proposition. Proposition 1.1. If limu→∞ M t, u /u ∞...

Extreme Points and Rotundity of Orlicz-sobolev Spaces

Smooth points of the unit sphere in Musielak-Orlicz function spaces equipped with the Luxemburg norm

There is given a criterion for an arbitrary element from the unit sphere of Musielak-Orlicz function space equipped with the Luxemburg norm to be a point of smoothness. Next, as a corollary, a criterion of smoothness of these spaces is given.

ISOMETRIC COPIES OF l AND l∞ IN ORLICZ SPACES EQUIPPED WITH THE ORLICZ NORM

Criteria in order that an Orlicz space equipped with the Orlicz norm contains a linearly isometric copy (or an order linearly isometric copy) of l1 (or l∞) are given.

On uniformly nonsquare points and nonsquare points of Orlicz spaces*

For Orlicz spaces endowed with the Orlicz norm and the Luxemburg norm, the criteria for uniformly nonsquare points and nonsquare points are given.