Sequentially compact sets in a class of generalized Orlicz spaces. (English) Zbl 1090.46011

Wang, Jincai

Commentat. Math. Univ. Carol. 43, No. 1, 119-132 (2002).

The author characterizes sequentially compact sets in a class of generalized Orlicz spaces \(L^ {(M^ {-1})}\). Note that those are Orlicz type spaces generated by the inverse function \(M^ {-1}\) to an Orlicz function \(M\) (i.e., \(M\) is even, continuous and convex on \((0,\infty )\) such that \(M(0)=0\), \(M(u)>0\) for all \(u\neq 0\) and \(\lim _ {u\to 0}\frac {M(u)}u=0\), \(\lim _ {u\to \infty }\frac {M(u)}u=\infty \)) satisfy the \(\Delta _ 2\)-condition.

Reviewer: Petr Gurka (Praha)

MSC:

46B20	Geometry and structure of normed linear spaces
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords:

generalized Orlicz space \(L^ {(M^ {-1})}\); \(\Delta _ 2\)-condition; sequentially compact set