Some Classes of Operators Related to ip/i-Hyponormal Operator

摘要

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].