On M-ideals of compact operators in Lorentz sequence spaces

Let X = d(nu, p) and Y = d(omega, q) be Lorentz sequence spaces. We investi gate when the space K(X, Y) of compact linear operators acting from X to Y forms or does not form an M-ideal tin 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 less than or equal to q, we establish a gene ral (essential) condition guaranteeing that K(X, Y) is not an M-ideal. In c ontrast, we prove that non-trivial M-ideals K(X, Y) do exist whenever 1 < p < q, and we give a description of them. (C) 2001 Academic Press.