Some Classes of Operators Related to <i>p</i>-Hyponormal Operator

Abstract

We introduce a new family of classes of operators termed as * p -paranormal operator, classes *A(p,p); p > 0 and *A(p,q); p , q > 0, parallel to p -paranormal operator and classes A(p,p); p > 0 and A(p,q); p , q > 0 introduced by M. Fujii, D. Jung, S. H. Lee, M. Y. Lee and R. Nakamoto [1]. We present a necessary and sufficient condition for p -hyponormal operator T∈B（H）to be * p -paranormal and the monotonicity of *A(p,q). We also present an alternative proof of a result of M. Fujii, et al . [1, Theorem 3.4].