Abstract:

Let T∈B(H). If  ||p≥|T|p≥|*|p for some p>0, then T is p-w-hyponormal. The quasinorma and subnormal relation of T and its Aluthge transform  are studied. It is proved that  is quasinormal if and only if T is quasinormal. An example that there exists a non subnormal p-w-hyponormal operator T and  subnormal is given.

Key words: p-w-hyponormal operator; normal operator; quasinormal operator; subnormal operator