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Schur property and lP isomorphic copies in Musielak–Orlicz sequence spaces

Published online by Cambridge University Press:  17 April 2009

B. Zlatanov
Department of Mathematics and Informatics, Plovdiv University, 24 “Tzar Assen” str, Plovdiv, 4000, Bulgaria
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The author shows that if the dual of a Musielak–Orlicz sequence space lΦ is a stabilized asymptotic l, space with respect to the unit vector basis, then lΦ is saturated with complemented copies of l1 and has the Schur property. A sufficient condition is found for the isomorphic embedding of lp spaces into Musielak–Orlicz sequence spaces.

Research Article
Copyright © Australian Mathematical Society 2007


[1]Alexopoulos, J., ‘On subspaces of non–reflexive Orlicz spaces’, Quaestiones Math. 21 (1998), 161175.CrossRefGoogle Scholar
[2]Bessaga, C. and Pelczynski, A., ‘On bases and unconditional convergence of series in Banach Spaces’, Studia Math. 17 (1958), 165174.CrossRefGoogle Scholar
[3]Blasco, O. and Gregori, P., ‘Type and cotype in Nakano sequence spaces l ({Pn})ʹ, (preprint).Google Scholar
[4]Dew, N., Asymptotic sructure of Banach spaces, (Ph.D. Thesis) (St. John's College University of Oxford, Oxford, 2002).Google Scholar
[5]Fuentes, F. and Hernandez, F., ‘On weighted Orlicz sequence spaces and their subspaces’, Rocky Mountain J. Math. 18 (1988), 585599.CrossRefGoogle Scholar
[6]Hudzik, H. and Kaminska, A., ‘On uniformly convex and B–convex Musielak–Orlicz spaces’, Comment. Math. Prace Mat. 25 (1985), 5975.Google Scholar
[7]Hudzik, H. and Maligranda, L., ‘Amemiya norm equals Orlicz norm in general’, Indag. Math. 11 (2000), 573585.CrossRefGoogle Scholar
[8]Kaminska, A. and Mastylo, M., ‘The Schur and (weak) Dunford–Pettis property in Banach lattices’, J. Austral. Math. Soc. 73 (2002), 251278.CrossRefGoogle Scholar
[9]Katirtzoglou, E., ‘Type and cotype in Musielak–Orlicz’, J. Math. Anal. Appl. 226 (1998), 431455.CrossRefGoogle Scholar
[10]Kircev, K. and Troyanski, S., ‘On Orlicz spaces associated to Orlicz functions not satisfying the Δ2–condition’, Serdica 1 (1975), 8895.Google Scholar
[11]Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces I, sequence spaces (Springer–Verlag, Berlin, 1977).Google Scholar
[12]Maligranda, L., ‘Indices and inerpolation’, Dissertationes Rozprawy Mat. 234 (1985), 49.Google Scholar
[13]Maurey, B., Milman, V.D. and Tomczak–Jaegermann, N., ‘Asymptotic infinite–dimensional theory of Banach spaces’, Oper. Theory Adv. Appl. 77 (1995), 149175.Google Scholar
[14]Milman, V.D. and Tomczak–Jaegermann, N., ‘Asymptotic lp spaces and bounded distortions’, Contemp. Math. 144 (1992), 173195.CrossRefGoogle Scholar
[15]Musielak, J., Orlicz spaces and modular spaces, Lecture Notes in Mathematics 1034 (Springer–Verlag, Berlin, 1983).CrossRefGoogle Scholar
[16]Peirats, V. and Ruiz, C., ‘On lP–copies in Musielak–Orlicz sequence spaces’, Arch. Math. Basel 58 (1992), 164173.CrossRefGoogle Scholar
[17]Yamamuro, S., ‘Modulared sequence spaces’, J. Fasc. Sci. Hokkaido Univ. Ser. 113 (1954), 112.Google Scholar
[18]Woo, J., ‘On modular sequence spaces’, Studia Math. 48 (1973), 271289.CrossRefGoogle Scholar