Investigating unit balls in Orlicz spaces endowed with p-Amemiya norm

The aim of this thesis is to interpret a topic that is generally in the scope of functional analysis from the point of view of abstract harmonic analysis. In general the set of extreme points of the closed unit ball B(X) of a Banach space X does not need to be closed. M. Wisła and A.S. Granero examined the closedness of the set of extreme points of the unit ball in Orlicz spaces for p-Amemiya norms which is a wider class of norms [7, 17]. In the thesis, the works of [7], [9] and [17] have been discussed in the context of a locally compact group G and the left Haar measure instead of a general measure space. First, p-Amemiya norms were introduced and significant properties of these norms were given. Then the closedness of the set of extreme points of the unit balls in Orlicz spaces has been examined with respect to the p-Amemiya norms for the cases of p=∞, p=1 and 1