Wang, Jincai Sequentially compact sets in a class of generalized Orlicz spaces. (English) Zbl 1090.46011 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 PDF BibTeX XML Cite \textit{J. Wang}, Commentat. Math. Univ. Carol. 43, No. 1, 119--132 (2002; Zbl 1090.46011) Full Text: EuDML EMIS OpenURL