On Properties of Class A(n) and n-Paranormal Operators. (12th March 2014)

• Record Type: Journal Article
• Authors: Li, Xiaochun; Gao, Fugen
• Other Names: Yang Changsen Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-03-12
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/629061
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Let n be a positive integer, and an operator T ∈ B ( ℋ ) is called a class A ( n ) operator if T 1 + n 2 / 1 + n ≥ | T | 2 and n -paranormal operator if T 1 + n x 1 / 1 + n ≥ | | T x | | for every unit vector x ∈ ℋ, which are common generalizations of class A and paranormal, respectively. In this paper, firstly we consider the tensor products for class A ( n ) operators, giving a necessary and sufficient condition for T ⊗ S to be a class A ( n ) operator when T and S are both non-zero operators; secondly we consider the properties for n -paranormal operators, showing that a n -paranormal contraction is the direct sum of a unitary and a C . 0 completely non-unitary contraction.