ON Subspaces OF NON-Reflexive Orlicz Spaces

摘要

Kadec and Pelcz#xFD;nski have shown that every non-reflexive subspace ofL1(#x3BC;) contains a copy ofl1complemented inL1(#x3BC;). On the other hand Rosenthal investigated the structure of reflexive subspaces ofL1(#x3BC;) and proved that such sub-spaces have non-trivial type. We show the same facts to hold true for a special class of non-reflexive Orlicz spaces. In particular we show that if F is an N-function in #x3B4;2with its complement G satisfying limt#x2192;#x221E;G(ct)/G(t)= #x221E;,then every non-reflexive subspace ofL*Fcontains a copy ofl1complemented inL*F.Furthermore we establish the fact that if F is an N-function in #x3B4;2with its complement G satisfying limt#x2192;#x221E;G(ct)/G(t)= #x221E;, then every reflexive subspace ofL*Fhas non-trivial type.