Bilinear Operators on Normed Linear Spaces

Pole DC	Wartość	Język
dc.contributor.author	Nakasho, Kazuhisa	-
dc.date.accessioned	2019-05-21T07:18:00Z	-
dc.date.available	2019-05-21T07:18:00Z	-
dc.date.issued	2019	-
dc.identifier.citation	Formalized Mathematics, Volume 27, Issue 1, Pages 15-23	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/7836	-
dc.description.abstract	The main aim of this article is proving properties of bilinear operators on normed linear spaces formalized by means of Mizar [1]. In the first two chapters, algebraic structures [3] of bilinear operators on linear spaces are discussed. Especially, the space of bounded bilinear operators on normed linear spaces is developed here. In the third chapter, it is remarked that the algebraic structure of bounded bilinear operators to a certain Banach space also constitutes a Banach space.In the last chapter, the correspondence between the space of bilinear operators and the space of composition of linear opearators is shown. We referred to [4], [11], [2], [7] and [8] in this formalization.	-
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	Lipschitz continuity	-
dc.subject	bounded linear operator	-
dc.subject	bilinear operator	-
dc.subject	algebraic structure	-
dc.subject	Banach space	-
dc.title	Bilinear Operators on Normed Linear Spaces	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2019-0002	-
dc.description.Affiliation	Yamaguchi University, Yamaguchi, Japan	-
dc.description.references	Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pak. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.	-
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dc.description.references	Kazuhisa Nakasho, Yuichi Futa, and Yasunari Shidama. Continuity of bounded linear operators on normed linear spaces. Formalized Mathematics, 26(3):231–237, 2018. doi:10.2478/forma-2018-0021.	-
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dc.identifier.eissn	1898-9934	-
dc.description.volume	27	-
dc.description.issue	1	-
dc.description.firstpage	15	-
dc.description.lastpage	23	-
dc.identifier.citation2	Formalized Mathematics	-
dc.identifier.orcid	0000-0003-1110-4342	-
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