dc.date.accessioned |
2019-01-22T20:34:53Z |
|
dc.date.available |
2019-01-22T20:34:53Z |
|
dc.date.issued |
2018 |
|
dc.identifier.issn |
0040-5779 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/147804 |
|
dc.description.abstract |
© 2018, Pleiades Publishing, Ltd. Let ϕ be a trace on the unital C*-algebra A and Mϕbe the ideal of the definition of the trace ϕ. We obtain a C*analogue of the quantum Hall effect: if P,Q ∈ A are idempotents and P − Q ∈ Mϕ, then ϕ((P − Q)2n+1) = ϕ(P − Q) ∈ R for all n ∈ N. Let the isometries U ∈ A and A = A*∈ A be such that I+A is invertible and U-A ∈ Mϕwith ϕ(U-A) ∈ R. Then I-A, I−U ∈ Mϕand ϕ(I−U) ∈ R. Let n ∈ N, dimH = 2n + 1, the symmetry operators U, V ∈ B(H), and W = U − V. Then the operator W is not a symmetry, and if V = V*, then the operator W is nonunitary. |
|
dc.relation.ispartofseries |
Theoretical and Mathematical Physics(Russian Federation) |
|
dc.subject |
C*-algebra |
|
dc.subject |
Hilbert space |
|
dc.subject |
idempotent |
|
dc.subject |
linear operator |
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dc.subject |
projection |
|
dc.subject |
quantum Hall effect |
|
dc.subject |
symmetry |
|
dc.subject |
trace |
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dc.subject |
trace-class operator |
|
dc.subject |
unitary operator |
|
dc.title |
Differences of Idempotents In C*-Algebras and the Quantum Hall Effect |
|
dc.type |
Article |
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dc.relation.ispartofseries-issue |
1 |
|
dc.relation.ispartofseries-volume |
195 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
557 |
|
dc.source.id |
SCOPUS00405779-2018-195-1-SID85046543571 |
|