Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Hyponormal powers of composition operators


Authors: Phillip Dibrell and James T. Campbell
Journal: Proc. Amer. Math. Soc. 102 (1988), 914-918
MSC: Primary 47B38; Secondary 47B20
DOI: https://doi.org/10.1090/S0002-9939-1988-0934867-X
MathSciNet review: 934867
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {T_i},i = 1,2$, be measurable transformations which define bounded composition operators $ {C_{{T_i}}}$ on $ {L^2}$ of a $ \sigma $-finite measure space. Denote their respective Radon-Nikodym derivatives by $ {h_i},i = 1,2$. The main result of this paper is that if $ {h_i} \circ {T_i} \leq {h_j},i,j = 1,2$, then for each of the positive integers $ m,n,p$ the operator $ {[C_{{T_1}}^mC_{{T_2}}^n]^p}$ is hyponormal. As a consequence, we see that the sufficient condition established by Harrington and Whitley for hyponormality of a composition operator is actually sufficient for all powers to be hyponormal.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B38, 47B20

Retrieve articles in all journals with MSC: 47B38, 47B20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0934867-X
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society