Asymptotically isometric copies of c0 in Musielak-Orlicz spaces

• Autorzy: Narloch A. , Szymaszkiewicz L.
• Języki publikacji: EN

Abstrakty

EN

Criteria in order that a Musielak-Orlicz function space Lφ as well as Musielak-Orlicz sequence space lφ contains an asymptotically isometric copy of c0 are given. These results extend some results of [Y.A. Cui, H. Hudzik, G. Lewicki, Order asymptotically isometric copies of c0 in the subspaces of order continuous elements in Orlicz spaces, Journal of Convex Analysis 21 (2014)] to Musielak-Orlicz spaces.

Słowa kluczowe

EN

Musielak-Orlicz space; Luxemburg norm; condition Delta2; asymptotically isometric copy of c0

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2014
• Tom: Vol. 34, no. 1
• Strony: 161--169
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Narloch A.

• University of Szczecin Institute of Mathematics Wielkopolska 15, 70-451 Szczecin, Poland

autor

Szymaszkiewicz L.

• University of Szczecin Institute of Mathematics Wielkopolska 15, 70-451 Szczecin, Poland

Bibliografia

• [1] G. Alherk, H. Hudzik, Copies of l1 and c0 in Musielak-Orlicz sequence spaces, Comment. Math. Univ. Carolinae 35 (1994) 1, 9–19.
• [2] S. Chen, Geometry of Orlicz spaces, Dissertationes Math. 356 (1996), 1–204.
• [3] Y.A. Cui, H. Hudzik, G. Lewicki, Order asymptotically isometric copies of c0 in the subspaces of order continuous elements in Orlicz spaces, Journal of Convex Analysis 21 (2014).
• [4] M. Denker, H. Hudzik, Uniformly non-ln(1) Musielak-Orlicz sequence spaces, Proc. Indian Acad. Sci. 101 (1991), 71–86.
• [5] P.N. Dowling, Isometric Copies of c0 and l∞ in Duals of Banach Spaces, J. Math. Anal. Appl. 244 (2000), 223–227.
• [6] P.N. Dowling, C.J. Lennard, B. Turett, Reflexivity and the fixed point property for nonexpansive maps, J. Math. Anal. Appl. 200 (1996), 653–662.
• [7] H. Hudzik, On some equivalent condition in Musielak-Orlicz spaces, Comment. Math. 24 (1984), 57–64.
• [8] A. Kaminska, Flat Orlicz-Musielak sequence spaces, Bull. Acad. Polon. Sci. Math. 30 (1982), 347–352.
• [9] M.A. Krasnoselski˘ı, Ya.B. Ruticki˘ı, Convex functions and Orlicz spaces, Groningen, 1961 (translation).
• [10] W.A.J. Luxemburg, Banach function spaces, Thesis, Delft, 1955.
• [11] J. Musielak, Orlicz spaces and modular spaces, Lecture Notes Math. 1034, Springer--Verlag, 1983.
• [12] M.M. Rao, Z.D. Ren, Theory of Orlicz spaces, Marcel Dekker, New York, 1991.