КФУ. Карточка публикации. On $\tau$-essentially invertibility of $\tau$-measurable operators

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ON $\TAU$-ESSENTIALLY INVERTIBILITY OF $\TAU$-MEASURABLE OPERATORS

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2019

Язык

армянский

Авторы, сотрудники КФУ

Бикчентаев Айрат Мидхатович, автор

Библиографическое описание на языке оригинала

Airat M. Bikchentaev, On $\tau$-essentially invertibility of $\tau$-measurable operators // Internat. J. Theor. Phys. 2019. V. 58. No 12. https://doi.org/10.1007/s10773-019-04111-w

Аннотация

Let ${\mathcal M}$ be a von Neumann algebra of operators on a Hilbert space and $\tau$ be a faithful normal semifinite trace on $\mathcal{M}$. Let $I$ be the unit of the algebra ${\mathcal M}$. A $\tau$-measurable operator $A$ is said to be {\it $\tau$-essentially right (or left) invertible} if there exists a $\tau$-measurable operator $B$ such that the operator $I-AB$ (or $I-BA$) is $\tau$-compact. A necessary and sufficient condition for an operator $A $ to be $\tau$-essentially left invertible is that $A^*A$ (or, equivalently, $\sqrt{A^*A}$) is $\tau$-essentially invertible. We present a sufficient condition that a $\tau$-measurable operator $A $ not be $\tau$-essentially left invertible. For $\tau$-measurable operators $A$ and $P=P^2$ the following conditions are equivalent: 1. $A$ is $\tau$-essential right inverse for $P$; 2. $A$ is $\tau$-essential left inverse for $P$; 3. $I-A, I-P $ are $\tau$-compact; 4. $PA$ is $\tau$-essential left inverse for $P$. For $\tau$-measurable operators $A=A^3$, $ B=B^3$ the following conditions are equivalent: 1. $B$ is $\tau$-essential right inverse for $A$; 2. $B$ is $\tau$-essential left inverse for~$A$. Pairs of faithful normal semifinite traces on $\mathcal{M}$ are considered.

Ключевые слова

Hilbert space, von Neumann algebra, normal weight, semifinite trace, measure topology, $\tau$-measurable operator, $\tau$-compact operator, rearrangement, $\tau$-essentially invertible operator, idempotent.

Название журнала

INT J THEOR PHYS

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https://repository.kpfu.ru/?p_id=202091

Файлы ресурса

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Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Бикчентаев Айрат Мидхатович	ru_RU
dc.date.accessioned	2019-01-01T00:00:00Z	ru_RU
dc.date.available	2019-01-01T00:00:00Z	ru_RU
dc.date.issued	2019	ru_RU
dc.identifier.citation	Airat M. Bikchentaev, On $\tau$-essentially invertibility of $\tau$-measurable operators // Internat. J. Theor. Phys. 2019. V. 58. No 12. https://doi.org/10.1007/s10773-019-04111-w	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/?p_id=202091	ru_RU
dc.description.abstract	INT J THEOR PHYS	ru_RU
dc.description.abstract	Let ${\mathcal M}$ be a von Neumann algebra of operators on a Hilbert space and $\tau$ be a faithful normal semifinite trace on $\mathcal{M}$. Let $I$ be the unit of the algebra ${\mathcal M}$. A $\tau$-measurable operator $A$ is said to be {\it $\tau$-essentially right (or left) invertible} if there exists a $\tau$-measurable operator $B$ such that the operator $I-AB$ (or $I-BA$) is $\tau$-compact. A necessary and sufficient condition for an operator $A $ to be $\tau$-essentially left invertible is that $A^A$ (or, equivalently, $\sqrt{A^A}$) is $\tau$-essentially invertible. We present a sufficient condition that a $\tau$-measurable operator $A $ not be $\tau$-essentially left invertible. For $\tau$-measurable operators $A$ and $P=P^2$ the following conditions are equivalent: 1. $A$ is $\tau$-essential right inverse for $P$; 2. $A$ is $\tau$-essential left inverse for $P$; 3. $I-A, I-P $ are $\tau$-compact; 4. $PA$ is $\tau$-essential left inverse for $P$. For $\tau$-measurable operators $A=A^3$, $ B=B^3$ the following conditions are equivalent: 1. $B$ is $\tau$-essential right inverse for $A$; 2. $B$ is $\tau$-essential left inverse for~$A$. Pairs of faithful normal semifinite traces on $\mathcal{M}$ are considered.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hilbert space	ru_RU
dc.subject	von Neumann algebra	ru_RU
dc.subject	normal weight	ru_RU
dc.subject	semifinite trace	ru_RU
dc.subject	measure topology	ru_RU
dc.subject	$\tau$-measurable operator	ru_RU
dc.subject	$\tau$-compact operator	ru_RU
dc.subject	rearrangement	ru_RU
dc.subject	$\tau$-essentially invertible operator	ru_RU
dc.subject	idempotent.	ru_RU
dc.title	On $\tau$-essentially invertibility of $\tau$-measurable operators	ru_RU
dc.type	Статьи в зарубежных журналах и сборниках	ru_RU