On M-Ideals of Compact Operators in Lorentz Sequence Spaces

AbstractLet X=d(v,p) and Y=d(w,q) be Lorentz sequence spaces. We 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). We show that K(X,Y) fails to be a non-trivial M-ideal whenever p=1 or p>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