Order continuous linear functionals on non-locally convex Orlicz spaces. (English) Zbl 0812.46017

Nowak, Marian

Commentat. Math. Univ. Carol. 33, No. 3, 465-475 (1992).

Summary: The space of all order continuous linear functionals on an Orlicz space \(L^ \varphi\) defined by an arbitrary (not necessarily convex) Orlicz function \(\varphi\) is described.

MSC:

46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B10	Duality and reflexivity in normed linear and Banach spaces
46B42	Banach lattices
46A80	Modular spaces

Keywords:

modular spaces; locally solid Riesz spaces; Köthe dual; order continuous linear functionals on an Orlicz space