Form of presentation  Articles in international journals and collections 
Year of publication  2019 
Язык  армянский 

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language 
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/s1077301904111w 
Annotation 
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 $IAB$ (or $IBA$) 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. $IA, IP $ 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. 
Keywords 
Hilbert space, von Neumann algebra, normal weight, semifinite trace, measure topology, $\tau$measurable operator, $\tau$compact operator, rearrangement, $\tau$essentially invertible operator, idempotent. 
The name of the journal 
INT J THEOR PHYS

Please use this ID to quote from or refer to the card 
https://repository.kpfu.ru/eng/?p_id=202091&p_lang=2 
Resource files  

Full metadata record 
Field DC 
Value 
Language 
dc.contributor.author 
Bikchentaev Ayrat Midkhatovich 
ru_RU 
dc.date.accessioned 
20190101T00:00:00Z 
ru_RU 
dc.date.available 
20190101T00:00:00Z 
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/s1077301904111w 
ru_RU 
dc.identifier.uri 
https://repository.kpfu.ru/eng/?p_id=202091&p_lang=2 
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 $IAB$ (or $IBA$) 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. $IA, IP $ 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 
Articles in international journals and collections 
ru_RU 
