KFU. Card publication. Inductive and projective limits of Banach spaces of measurable functions with order unities with respect to power parameter

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INDUCTIVE AND PROJECTIVE LIMITS OF BANACH SPACES OF MEASURABLE FUNCTIONS WITH ORDER UNITIES WITH RESPECT TO POWER PARAMETER

Form of presentation

Articles in international journals and collections

Year of publication

2016

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Authors, employees of KFU

Novikov Andrey Andreevich, author

Bibliographic description in the original language

Novikov A.A, Eskandarian Z., Inductive and projective limits of Banach spaces of measurable functions with order unities with respect to power parameter//Russian Mathematics. - 2016. - Vol.60, Is.10. - P.67-71.

Annotation

We prove that a measurable function f is bounded and invertible if and only if there exist at least two equivalent norms by order unit spaces with order unities fα and fβ with α > β > 0. We show that it is natural to understand the limit of ordered vector spaces with order unities fα (α approaches to infinity) as a direct sum of one inductive and one projective limits. We also obtain some properties for the corresponding limit topologies.

Keywords

inductive limit, projective limit, initial topology, final topology, order unit space, measurable functions, Banach space, Fréchet space, locally convex space

The name of the journal

Russian Mathematics

URL

https://www.scopus.com/inward/record.uri?eid=2-s2.0-84988884463&partnerID=40&md5=8150a6bf326494a5ee084432b5217449

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

https://repository.kpfu.ru/eng/?p_id=148082&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Novikov Andrey Andreevich	ru_RU
dc.date.accessioned	2016-01-01T00:00:00Z	ru_RU
dc.date.available	2016-01-01T00:00:00Z	ru_RU
dc.date.issued	2016	ru_RU
dc.identifier.citation	Novikov A.A, Eskandarian Z., Inductive and projective limits of Banach spaces of measurable functions with order unities with respect to power parameter//Russian Mathematics. - 2016. - Vol.60, Is.10. - P.67-71.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=148082&p_lang=2	ru_RU
dc.description.abstract	Russian Mathematics	ru_RU
dc.description.abstract	We prove that a measurable function f is bounded and invertible if and only if there exist at least two equivalent norms by order unit spaces with order unities fα and fβ with α > β > 0. We show that it is natural to understand the limit of ordered vector spaces with order unities fα (α approaches to infinity) as a direct sum of one inductive and one projective limits. We also obtain some properties for the corresponding limit topologies.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	inductive limit	ru_RU
dc.subject	projective limit	ru_RU
dc.subject	initial topology	ru_RU
dc.subject	final topology	ru_RU
dc.subject	order unit space	ru_RU
dc.subject	measurable functions	ru_RU
dc.subject	Banach space	ru_RU
dc.subject	Fréchet space	ru_RU
dc.subject	locally convex space	ru_RU
dc.title	Inductive and projective limits of Banach spaces of measurable functions with order unities with respect to power parameter	ru_RU
dc.type	Articles in international journals and collections	ru_RU