Property (t) and perturbations

In this paper we study the properties of property ( t ), which is introduced by Rashid. We investigate the property ( t ) in connection with Weyl type theorems, and establish sufficient and necessary conditions for which property ( t ) holds. Especially, we obtain the equivalence of a -Weyl’s theore...

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Bibliographic Details
Published inRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 113; no. 2; pp. 1417 - 1427
Main Authors Shen, Junli, Ji, Guoxing
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2019
Subjects
Applications of Mathematics
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
)
Secondary 47A10
Perturbation
Property
Primary 47B20
Weyl type theorem
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Summary:In this paper we study the properties of property ( t ), which is introduced by Rashid. We investigate the property ( t ) in connection with Weyl type theorems, and establish sufficient and necessary conditions for which property ( t ) holds. Especially, we obtain the equivalence of a -Weyl’s theorem and property ( t ) without the condition that T is a -polaroid, which improves a corresponding result of Rashid (Mediterr J Math 11:1–16, 2014 ). We also study the stability of property ( t ) under perturbations by nilpotent operators, by finite rank operators, by quasi-nilpotent operators and by Riesz operators commuting with T .
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-018-0555-3