Necessary and sufficient conditions are given for Orlicz sequence spaces equipped with the Orlicz norm to be uniformly rotund in a weakly compact set of directions, using only conditions on the generating function of the space.
Orthogonality in inner products is a binary relation that can be expressed in many ways without explicit mention to the inner product of the space. Great part of such definitions have also sense in normed linear spaces. This simple observation is at the base of many concepts of orthogonality in these more general structures. Various authors introduced such concepts over the last fifty years, although the origins of some of the most interesting results that can be obtained for these generalized concepts...
Some generalized notions of James' orthogonality and orthogonality in the Pythagorean sense are defined and studied in the case of generalized normed spaces derived from generalized inner products.