Extreme Points and Strongly Extreme Points in Orlicz Spaces Equipped with the Orlicz Norm

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.

The criteria of strongly exposed points in Orlicz spaces

In Orlicz spaces, the necessary and sufficient conditions of strongly exposed points are 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.