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.
"On Properties of Class and -Paranormal Operators." Abstr. Appl. Anal. 2014 (SI43) 1 - 5, 2014. https://doi.org/10.1155/2014/629061