dc.contributor |
Казанский федеральный университет |
|
dc.contributor.author |
Bikchentaev Airat Midkhatovich |
en |
dc.date.accessioned |
2023-02-22T06:38:17Z |
|
dc.date.available |
2023-02-22T06:38:17Z |
|
dc.date.issued |
2023 |
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dc.identifier.citation |
Bikchentaev A.M. The algebra of thin measurable operators is directly finite/ A.M. Bikchentaev // Constructive Mathematical Analysis. - 2023. -
V. 6, no 1. - P. 1-5. |
en |
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/175023 |
|
dc.description.abstract |
Let $\mathcal{M}$ be a semifinite von Neumann algebra on a Hilbert space $\cH$ equipped with a faithful normal semifinite trace $\tau$, $S(\mathcal{M},\tau)$ be the ${}^*$-algebra of all $\tau$-measurable operators. Let $S_0(\mathcal{M},\tau)$ be the ${}^*$-algebra of all $\tau$-compact operators and
$T(\mathcal{M},\tau)=S_0(\mathcal{M},\tau)+\mathbb{C}I$ be the ${}^*$-algebra of all operators $X=A+\lambda I$
with $A\in S_0(\mathcal{M},\tau)$ and $\lambda \in \mathbb{C}$. We prove that every operator of $T(\mathcal{M},\tau)$ that is left-invertible in $T(\mathcal{M},\tau)$ is in fact invertible in $T(\mathcal{M},\tau)$.
It is a generalization of Sterling Berberian theorem (1982) on the subalgebra of thin operators in $\cB (\cH)$.
For the singular value function $\mu(t; Q)$ of $Q=Q^2\in S(\mathcal{M},\tau)$ we have $\mu(t; Q)\in \{0\}\bigcup
[1, +\infty)$ for all $t)0$. It gives the positive answer to the question posed by Daniyar Mushtari in 2010. |
en |
dc.language.iso |
en |
|
dc.relation.ispartofseries |
Constructive Mathematical Analysis |
en |
dc.rights |
открытый доступ |
|
dc.subject |
Hilbert space |
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dc.subject |
von Neumann algebra |
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dc.subject |
semifinite trace |
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dc.subject |
$\tau$-measurable operator |
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dc.subject |
$\tau$-compact operator |
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dc.subject |
singular value function |
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dc.subject |
idempotent |
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dc.title |
The algebra of thin measurable operators is directly finite |
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dc.type |
Article |
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dc.contributor.org |
Институт математики и механики им. Н.И. Лобачевского |
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dc.description.pages |
1-5 |
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dc.relation.ispartofseries-issue |
1 |
|
dc.relation.ispartofseries-volume |
6 |
|
dc.pub-id |
276828 |
|
dc.identifier.doi |
10.33205/cma.1181495 |
|