Continuity of Multilinear Operator on Normed Linear Spaces

Pole DC	Wartość	Język
dc.contributor.author	Nakasho, Kazuhisa	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2019-05-21T07:18:02Z	-
dc.date.available	2019-05-21T07:18:02Z	-
dc.date.issued	2019	-
dc.identifier.citation	Formalized Mathematics, Volume 27, Issue 1, Pages 61-65	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/7840	-
dc.description.abstract	In this article, various definitions of contuity of multilinear operators on normed linear spaces are discussed in the Mizar formalism [4], [1] and [2]. In the first chapter, several basic theorems are prepared to handle the norm of the multilinear operator, and then it is formalized that the linear space of bounded multilinear operators is a complete Banach space.In the last chapter, the continuity of the multilinear operator on finite normed spaces is addressed. Especially, it is formalized that the continuity at the origin can be extended to the continuity at every point in its whole domain. We referred to [5], [11], [8], [9] in this formalization.	-
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	Lipschitz continuity	-
dc.subject	bounded linear operators	-
dc.subject	multilinear operators	-
dc.subject	Banach space	-
dc.title	Continuity of Multilinear Operator on Normed Linear Spaces	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2019-0006	-
dc.description.Affiliation	Kazuhisa Nakasho - Yamaguchi University, Yamaguchi, Japan	-
dc.description.Affiliation	Yasunari Shidama - Shinshu University, Nagano, Japan	-
dc.description.references	Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.	-
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dc.description.references	Miyadera Isao. Functional Analysis. Riko-Gaku-Sya, 1972.	-
dc.description.references	Kazuhisa Nakasho, Yuichi Futa, and Yasunari Shidama. Implicit function theorem. Part I. Formalized Mathematics, 25(4):269–281, 2017. doi:10.1515/forma-2017-0026.	-
dc.description.references	Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269–275, 2004.	-
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dc.description.references	Laurent Schwartz. Calcul différentiel, tome 2. Analyse. Hermann, 1997.	-
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dc.description.references	Kosaku Yoshida. Functional Analysis. Springer, 1980.	-
dc.identifier.eissn	1898-9934	-
dc.description.volume	27	-
dc.description.issue	1	-
dc.description.firstpage	61	-
dc.description.lastpage	65	-
dc.identifier.citation2	Formalized Mathematics	-
dc.identifier.orcid	0000-0003-1110-4342	-
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