Some Classes of Operators Related to p-Hyponormal Operator

Md. Ilyas, Reyaz Ahmad

Al-Ain University of Science and Technology, Al Ain & Abu Dhabi, UAE.
Department of Mathematics, Gaya College, Gaya, Bihar, India.

DOI: 10.4236/apm.2012.26063                

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].

Keywords

p-Hyponormal Operator; Monotonicity; Class of Operators *A(p, q); *Paranormal Operator; *p-Paranormal Operator

Conflicts of Interest

The authors declare no conflicts of interest.

References

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