KFU. Card publication. C∗-algebra Positive Element Invertibility Criteria in Terms of L1-norms Equivalence and L∞-norms Equivalence

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FEDERAL UNIVERSITY

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C∗-ALGEBRA POSITIVE ELEMENT INVERTIBILITY CRITERIA IN TERMS OF L1-NORMS EQUIVALENCE AND L∞-NORMS EQUIVALENCE

Form of presentation

Articles in Russian journals and collections

Year of publication

2019

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Authors, employees of KFU

Novikov Andrey Andreevich, author

Bibliographic description in the original language

C∗-algebra Positive Element Invertibility Criteria in Terms of L1-norms Equivalence and L∞-norms Equivalence // Lobachevskii Journal of Mathematics, 2019, Vol. 40, No. 5, pp. 549–552. c Pleiades Publishing, Ltd., 2019.

Annotation

Abstract—We prove that the L1-norms associated with a positive elements aα is equivalent to the L1-norm associated with a positive element aβ if and only if it is equivalent to the natural norm of a C∗-algebra, which means the invertibility of a in the case of unital C∗-algebra. The same propositions are proved for L∞-norms associated with positive element aα and aβ.

Keywords

C∗-algebra, von Neumann algebra, invertibility, L1-norm, noncommu- tative, positive element.

The name of the journal

Lobachevskii Journal of Mathematics

URL

https://link.springer.com/article/10.1134%2FS1995080219050159

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=199761&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Novikov Andrey Andreevich	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	C∗-algebra Positive Element Invertibility Criteria in Terms of L1-norms Equivalence and L∞-norms Equivalence // Lobachevskii Journal of Mathematics, 2019, Vol. 40, No. 5, pp. 549–552. c Pleiades Publishing, Ltd., 2019.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=199761&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics	ru_RU
dc.description.abstract	Abstract—We prove that the L1-norms associated with a positive elements aα is equivalent to the L1-norm associated with a positive element aβ if and only if it is equivalent to the natural norm of a C∗-algebra, which means the invertibility of a in the case of unital C∗-algebra. The same propositions are proved for L∞-norms associated with positive element aα and aβ.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	C∗-algebra	ru_RU
dc.subject	von Neumann algebra	ru_RU
dc.subject	invertibility	ru_RU
dc.subject	L1-norm	ru_RU
dc.subject	noncommu- tative	ru_RU
dc.subject	positive element.	ru_RU
dc.title	C∗-algebra Positive Element Invertibility Criteria in Terms of L1-norms Equivalence and L∞-norms Equivalence	ru_RU
dc.type	Articles in Russian journals and collections	ru_RU