Abstract
Generalized Orlicz–Lorentz sequence spaces λφ generated by Musielak-Orlicz functions φ satisfying some growth and regularity conditions (see [28] and [33]) are investigated. A regularity condition δλ2 for φ is defined in such a way that it guarantees many positive topological and geometric properties of λφ. The problems of the Fatou property, the order continuity and the Kadec–Klee property with respect to the uniform convergence of the space λφ are considered. Moreover, some embeddings between λφ and their two subspaces are established and strict monotonicity as well as lower and upper local uniform monotonicities are characterized. Finally, necessary and sufficient conditions for rotundity of λφ, their subspaces of order continuous elements and finite dimensional subspaces are presented. This paper generalizes the results from [19], [4] and [17]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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