设T∈B(H),如果对某个P〉0都有│T│P≥│T│P≥│T*│P,则称丁是p-弱亚正规算子。本文主要研究了p-弱亚正规算子T和它的Aluthge变换T的拟正规性和次正规性之间的关系,证明了T是拟正规算子当且仅当T是拟正规算子。最后,举例得到了存在非次正规的p-弱亚正规算子T而T是次正规的。
Let T ∈B (H). If │T│P≥│T│P≥│T*│P for some p 〉 0, then T is p-w-hyponormal. The quasinorma and sub- normal relation of T and its Aluthge transform T are studied. It is proved that T is quasinormal if and only if T is quasi- normal. An example that there exists a non subnormal p-w-hyponormal operator T and T subnormal is given.