LIFTING NONTOPOLOGICAL DIVISORS OF ZERO MODULO THE COMPACT-OPERATORS

This paper provides the first examples of non-semiFredholm operators S on a Banach space such that the left or right multiplication operator s R bar arrow pointing right SR or R bar arrow pointing right RS defin e linear embeddings of the corresponding Calkin algebra into itself. F or instance, if S is a bounded linear operator on C(0, 1) with closed range such that Ker S approximately l1, then there is a constant c > 0 with dist (SR, K(C(0, 1))) greater-than-or-equal-to c dist(R, K(C(0, 1))) for all bounded operators R is-an-element-of L(C(0, 1)). Here K(C (0, 1)) stands for the compact operators on C(0, 1). Moreover, if S:L1 --> L1 has closed range and L1/Im S contains no copies of l1, then th ere is a constant c > 0 such that dist(RS, W(L1)) greater-than-or-equa l-to c dist(R, W(L1)) for all R is-an-element-of L(L1). Here W(L1) den otes the weakly compact operators on L1. (C) 1994 Academic Press, Inc.