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Abstract and Applied Analysis
Volume 2014, Article ID 629061, 5 pages
Research Article

On Properties of Class and -Paranormal Operators

College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, China

Received 26 December 2013; Accepted 6 February 2014; Published 12 March 2014

Academic Editor: Changsen Yang

Copyright © 2014 Xiaochun Li and Fugen Gao. 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.


Let be a positive integer, and an operator is called a class operator if and -paranormal operator if for every unit vector , which are common generalizations of class and paranormal, respectively. In this paper, firstly we consider the tensor products for class operators, giving a necessary and sufficient condition for to be a class operator when and are both non-zero operators; secondly we consider the properties for -paranormal operators, showing that a -paranormal contraction is the direct sum of a unitary and a completely non-unitary contraction.