赋Φ-Amemiya范数的Orlicz空间包含序渐进等距c0复本

The Orlicz space equipped with the Φ-Amemiya norm contains an order asymptotically isometric copy of c0

在Orlicz空间中,我们引进了一个与Luxemburg范数等价的新范数——赋Φ-Amemiya范数:||x||Φ,Φ1=inf{1/k(1+Φ(IΦ1(kx)))}.并证明了由此范数构成的Orlicz函数空间{LΦ,Φ1,||·||Φ,Φ1}是Banach空间.据此得到了赋Φ-Amemiya范数的Olicz空间包含序渐近等距c0复本的条件.

In Orlicz space,a new norm that is equivalent to the Luxemburg norm is introduced.It is called theΦ-Amemiya norm:||x||Φ,Φ1=inf{1/k(1+Φ(IΦ1(kx)))}.It is shown,furthermore,that the Orlicz function space equipped with this norm{LΦ,Φ1,||·||Φ,Φ1}is a Banach space.Hence,this paper demonstrates the conditions for the Orlicz space with theΦ-Amemiya norm to contain an asymptotically isometric copy of c0.