ON SEMI m-HYPONORMAL WEIGHTED SHIFT OPERATORS

摘要

In this paper, we study semi m-hyponormal operator which is a special case of mhyponormal operator. It is very obvious that every semi m-hyponormal weighted shift operator is semi-weakly m-hyponormal. We have shown that hyponormal weighted shift operators, which are semi m-hyponormal, must have positive determinant coefficients (p.d.c) of order m (m ≥ 2). In particular, it is proved that every hyponormal weighted shift with first two equal weights cannot be semi mhyponormal without being flat.