Uniformly non-l
n
(1)
Musielak-Orlicz sequence spaces |
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Authors: | Manfred Denker Henryk Hudzik |
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Institution: | 1. Institut für Mathematische Stochastik, Universit?t G?ttingen, Lotzestr. 13, D-3400, G?ttingen, Germany 2. Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60-769, Poznan, Poland
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Abstract: | We give a necessary and sufficient condition for the uniformly non-l
n
(1)
property of Musielak-Orlicz sequence spacesl
Φ generated by a sequence Φ=(ϕn:n⩾l) of finite Orlicz functions such that
for eachn∈ℕ. As a result, forn
0⩾2, there exist spacesl
Φ which are only uniformly non-l
n
(1)
forn⩾n
0. Moreover we obtain a characterization of uniformly non-l
n
(1)
and reflexive Orlicz sequence spaces over a wide class of purely atomic measures and of uniformly non-l
n
(1)
Nakano sequence spaces. This extends a result of Luxemburg in 19].
Submitted in memory of Professor W. Orlicz |
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Keywords: | Musielak-Orlicz sequence space uniformly non-l n (1) reflexivity convexity |
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