A criterion for strongly exposed points of the unit ball $B\left(l_M\right)$ in Musielak-Orlicz sequence spaces $l_M$ equipped with Orlicz norm is given.

We study the superposition operator f on on the space ac 0 of sequences almost converging to zero. Conditions are derived for which f has a representation of the form f x = a+bx +g x, for all x ∈ ac 0 with a = f 0, b ∈ D(ac 0), g a superposition operator from ℓ∞ into I(ac 0), D(ac 0) = {z: zx ∈ ac 0 for all x ∈ ac 0}, and I(ac 0) the maximal ideal in ac 0. If f is generated by a function f of a real variable, then f is linear. We consider the conditions for which a bounded function f generates f...

Support functionals in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm are completely characterized. An explicit formula for regular support functionals is given. For obtaining a characterization of singular support functionals a generalized Banach limit is applied. Some necessary and sufficient conditions for smooothness of these spaces are given, too.