A NOTE ON n-PERINORMAL OPERATORS

doi:10.1016/S0252-9602(13)60136-8

Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (1): 194-198.doi: 10.1016/S0252-9602(13)60136-8

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A NOTE ON n-PERINORMAL OPERATORS

ZUO Hong-Liang, ZUO Fei

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

Received:2012-08-30 Revised:2013-01-22 Online:2014-01-20 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).

Abstract

Abstract:

The study of operators satisfying σ_ja(T) = σ_a(T) is of significant interest. Does σ_ja(T) = σ_a(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 σ_ja(T)\{0} = σ_a(T)\{0}. We also consider tensor product of n-perinormal operators.

Key words: n-perinormal operators, approximate point spectrum, joint approximate point spectrum, tensor product

CLC Number:

47B20

ZUO Hong-Liang, ZUO Fei. A NOTE ON n-PERINORMAL OPERATORS[J].Acta mathematica scientia,Series B, 2014, 34(1): 194-198.

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A NOTE ON n-PERINORMAL OPERATORS

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