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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 | |
dc.subject | Hilbert space | |
dc.subject | hyponormal operator | |
dc.subject | idempotent | |
dc.subject | invertibility | |
dc.subject | nuclear operator | |
dc.subject | projection | |
dc.subject | similarity | |
dc.subject | symmetry | |
dc.subject | trace | |
dc.subject | tripotent | |
dc.title | Tripotents in algebras: Invertibility and hyponormality | |
dc.type | Article | |
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 |