\(E^ \Phi\) and \(h^ \Phi\) fail to be \(M\)-ideals in \(L^ \Phi\) and \(\ell^ \Phi\) in the case of the Orlicz norm

DOI10.1007/BF02850836zbMath0827.46023MaRDI QIDQ1897635

Henryk Hudzik, Shutao Chen

Publication date: 17 December 1995

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

zbMATH Keywords

Luxemburg normOrlicz norm\(M\)-ideal\(\Delta_ 2\)-conditionnorm-preserving extensionlinear continuous regular functional

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Sequence spaces (including Köthe sequence spaces) (46A45) Geometry and structure of normed linear spaces (46B20) Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) Banach sequence spaces (46B45)

Related Items (2)

Orlicz spaces with a \(o\)-\(O\) type structure ⋮ Banach lattices with order isometric copies of \(l^\infty\)

Cites Work

• \(M\)-ideals in Banach spaces and Banach algebras
• Orlicz spaces and modular spaces
• M-structure and the Banach-Stone theorem
• Linear functionals on Orlicz sequence spaces without local convexity
• New classes of Banach spaces which are M-ideals in their biduals
• Generalized modular spaces
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