TITLE:
Some Classes of Operators Related to p-Hyponormal Operator
AUTHORS:
Md. Ilyas, Reyaz Ahmad
KEYWORDS:
p-Hyponormal Operator; Monotonicity; Class of Operators *A(p, q); *Paranormal Operator; *p-Paranormal Operator
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.6,
November
26,
2012
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].