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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Published in | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 113; no. 2; pp. 1417 - 1427 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
01.04.2019
|
Subjects | |
Online Access | Get full text |
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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
. |
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ISSN: | 1578-7303 1579-1505 |
DOI: | 10.1007/s13398-018-0555-3 |