On Properties of Class A(n) and n‐Paranormal Operators

Xiaochun Li and Fugen Gao

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: Let n be a positive integer, and an operator T ∈ B(ℋ) is called a class A(n) operator if T1+n2/1+n≥|T|2 and n‐paranormal operator if T1+nx1/1+n≥||Tx|| 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.

Date: 2014
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https://doi.org/10.1155/2014/629061

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:629061

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