Properties of p-ω-hyponormal operators

The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In fact, it is a generalization of approximate point spectrum properties of ω-hyponormal operators. The relation of spectra and numerical range of p-ω-hyponormal operators is obtained. On the other hand, for p-ω-hyponormal operators T, it is showed that if T is normal, then T is also normal.