dc.contributor.author |
Bikchentaev A. |
|
dc.date.accessioned |
2018-09-18T20:34:40Z |
|
dc.date.available |
2018-09-18T20:34:40Z |
|
dc.date.issued |
2014 |
|
dc.identifier.issn |
1995-0802 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/141321 |
|
dc.description.abstract |
© 2014, Pleiades Publishing, Ltd. Let A be a unital algebra over complex field ℂ, I be the unit of A. An element A ∈ A is called tripotent if A3 = A. Let Atri = {A ∈ A: A3 = A}. We show that A ∈ Atri if and only if I ± A − A2 ∈ Atri. We study invertibility properties of elements I + λA with A ∈ Atri and λ ∈ ℂ \ {−1,1}. Let X be a Banach space with the approximation property and A, B ∈ B(X)tri. If A − B is a nuclear operator then tr(A − B) ∈ ℂ. We show that if H is a Hilbert space and an operator A ∈ B(H)tri is hyponormal or cohyponormal then A = A*. We also prove that every A ∈ B(H)tri similar to a Hermitian tripotent. |
|
dc.relation.ispartofseries |
Lobachevskii Journal of Mathematics |
|
dc.subject |
algebra |
|
dc.subject |
Banach space |
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dc.subject |
Hilbert space |
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dc.subject |
hyponormal operator |
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dc.subject |
idempotent |
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dc.subject |
invertibility |
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dc.subject |
nuclear operator |
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dc.subject |
projection |
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dc.subject |
similarity |
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dc.subject |
symmetry |
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dc.subject |
trace |
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dc.subject |
tripotent |
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dc.title |
Tripotents in algebras: Invertibility and hyponormality |
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dc.type |
Article |
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dc.relation.ispartofseries-issue |
3 |
|
dc.relation.ispartofseries-volume |
35 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
281 |
|
dc.source.id |
SCOPUS19950802-2014-35-3-SID84907048244 |
|