J4 ›› 2013, Vol. 48 ›› Issue (09): 68-72.

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The normality of p-w-hyponormal operators  

YANG Hua1,2, CHANG Huan3, JI Guo-xing2   

  1. 1. School of Science, Anyang Institute of Technology, Anyang 455000, Henan, China;
    2. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China;
    3. Anyang Hitech Zone High School, Anyang 455000, Henan, China
  • Received:2012-04-26 Online:2013-09-20 Published:2013-09-25

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

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