Acta mathematica scientia, Series B >
A NOTE ON n-PERINORMAL OPERATORS
Received date: 2012-08-30
Revised date: 2013-01-22
Online published: 2014-01-20
Supported by
This work is partially supported by NNSF (11226185, 11201126) and the Basic Science and Technological Frontier Project of Henan Province (132300410261).
The study of operators satisfying σja(T) = σa(T) is of significant interest. Does σja(T) = σa(T) for n-perinormal operator T ∈B(H)? This question was raised by Mecheri and Braha [Oper. Matrices 6 (2012), 725–734]. In the note we construct a
counterexample to this question and obtain the following result: if T is a n-perinormal operator in B(H), then σja(T)\{0} = σa(T)\{0}. We also consider tensor product of n-perinormal operators.
ZUO Hong-Liang , ZUO Fei . A NOTE ON n-PERINORMAL OPERATORS[J]. Acta mathematica scientia, Series B, 2014 , 34(1) : 194 -198 . DOI: 10.1016/S0252-9602(13)60136-8
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