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On some geometric and topological properties of generalized Orlicz–Lorentz sequence spaces
Author(s) -
Foralewski Paweł,
Hudzik Henryk,
Szymaszkiewicz Lucjan
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510594
Subject(s) - linear subspace , mathematics , lorentz transformation , sequence (biology) , monotonic function , lorentz space , pure mathematics , sequence space , order (exchange) , convergence (economics) , space (punctuation) , property (philosophy) , topology (electrical circuits) , mathematical analysis , combinatorics , banach space , linguistics , philosophy , physics , finance , classical mechanics , epistemology , biology , economics , genetics , economic growth
Generalized Orlicz–Lorentz sequence spaces λ φ generated by Musielak‐Orlicz functions φ satisfying some growth and regularity conditions (see [28] and [33]) are investigated. A regularity condition δ λ 2 for φ is defined in such a way that it guarantees many positive topological and geometric properties of λ φ . The problems of the Fatou property, the order continuity and the Kadec–Klee property with respect to the uniform convergence of the space λ φ are considered. Moreover, some embeddings between λ φ 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 λ φ , 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)