STRICTLY SINGULAR OPERATORS ON L-p SPACES AND INTERPOLATION

摘要

We study the class V-p of strictly singular non-compact operators on L-p spaces. This allows us to obtain interpolation results for strictly singular operators on L-p spaces. Given 1 <= p < q <= infinity, it is shown that if an operator T bounded on L-p and L-q is strictly singular on L-r for some p <= r <= q, then it is compact on L-s for every p < s < q.