Research Article
Open Access
Extensions of the results on powers of
-hyponormal and
-hyponormal operators
- Changsen Yang1Email author and
- Jiangtao Yuan1
Journal of Inequalities and Applications20062006:36919
https://doi.org/10.1155/JIA/2006/36919
© C. Yang and J. Yuan 2006
Received: 22 November 2004
Accepted: 10 May 2005
Published: 9 March 2006
Abstract
Firstly, we will show the following extension of the results on powers of
-hyponormal and
-hyponormal operators: let
and
be positive integers, if
is
-hyponormal for
, then: (i) in case
,
and
hold, (ii) in case
,
and
hold. Secondly, we will show an estimation on powers of
-hyponormal operators for
which implies the best possibility of our results. Lastly, we will show a parallel estimation on powers of
-hyponormal operators as follows: let
, then the following hold for each positive integer
and
: (i) there exists a log-hyponormal operator
such that
, (ii) there exists a
-hyponormal operator
such that
.
Authors’ Affiliations
(1)
College of Mathematics and Information Science, Henan Normal University
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Copyright
© C. Yang and J. Yuan 2006
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
