On M-Ideals of Compact Operators in Lorentz Sequence Spaces1

Let X = d v p and Y = d w q be Lorentz sequence spaces.W e investigate when the space K X Y of compact linear operators acting from X to Y forms or does not form an M-ideal (in the space of bounded linear operators).W e show that K X Y fails to be a non-trivial M-ideal whenever p = 1 orp > q.In the case when 1 < p ≤ q, we establish a general (essential) condition guaranteeing that K X Y is not an M-ideal.In contrast, we prove that non-trivial M-ideals K X Y do exist whenever 1 < p < q, and we give a description of them.