The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces

Abstract EN

It is well known that the modulus of nearly uniform smoothness related with the fixed point property is important in Banach spaces.

In this paper, we prove that the modulus of nearly uniform smoothness in Köthe sequence spaces without absolutely continuous norm is ΓX(t)=t.

Meanwhile, the formula of the modulus of nearly uniform smoothness in Orlicz sequence spaces equipped with the Luxemburg norm is given.

As a corollary, we get a criterion for nearly uniform smoothness of Orlicz sequence spaces equipped with the Luxemburg norm.

Finally, the equivalent conditions of R(a,l(Φ))<1+a and RW(a,l(Φ))<1+a are given.