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dc.contributor.author | Bikchentaev A. | |
dc.contributor.author | Ivanshin P. | |
dc.date.accessioned | 2020-01-21T20:31:08Z | |
dc.date.available | 2020-01-21T20:31:08Z | |
dc.date.issued | 2019 | |
dc.identifier.issn | 0020-7748 | |
dc.identifier.uri | https://dspace.kpfu.ru/xmlui/handle/net/157316 | |
dc.description.abstract | © 2019, Springer Science+Business Media, LLC, part of Springer Nature. We introduce the class K A,ϕ = { A∈ A: ϕ(A k ) = ϕ(A) for all k∈ ℕ} for a linear functional ϕ on an algebra A and consider the properties of this class. Also we prove the “0–1 number lemma”: if a set {zk}k=1n⊂ℂ is such that z1+…+zn=z12+…+zn2=⋯=z1n+1+…+znn+1, then z k ∈{0,1}, for all k = 1,2,…,n. This lemma helps us to show that { ϕ(A) : A∈ K A,ϕ } = { 0 , 1 , … , n} and det(A) ∈{0,1} for A= M n (ℂ) and ϕ = tr, the canonical trace. We have A = P + Z where P is a projection and Z is a nilpotent for any A∈ K A,ϕ . Assume that for a trace class operator A there exists a constant C∈ ℂ such that tr(A k ) = C for all k∈ ℕ. Then C∈ ℕ⋃ { 0 } and the spectrum σ(A) is a subset of {0,1}. Finally we give the description of all the elements of the class K A,ϕ for M 2 (ℂ). | |
dc.relation.ispartofseries | International Journal of Theoretical Physics | |
dc.subject | C -algebra ∗ | |
dc.subject | Determinant | |
dc.subject | Hilbert space | |
dc.subject | Idempotent | |
dc.subject | Linear functional | |
dc.subject | Normed algebra | |
dc.subject | Spectrum | |
dc.subject | State | |
dc.subject | Trace class operator | |
dc.subject | Tracial functional | |
dc.subject | Vandermonde matrix | |
dc.subject | W -algebra ∗ | |
dc.title | On Operators all of Which Powers have the same Trace | |
dc.type | Article | |
dc.collection | Публикации сотрудников КФУ | |
dc.source.id | SCOPUS00207748-2019-SID85062450757 |