Continuity of Bounded Linear Operators on Normed Linear Spaces

Pole DC	Wartość	Język
dc.contributor.author	Nakasho, Kazuhisa	-
dc.contributor.author	Futa, Yuichi	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2019-03-04T10:34:25Z	-
dc.date.available	2019-03-04T10:34:25Z	-
dc.date.issued	2018/10/01	-
dc.identifier.citation	Formalized Mathematics, Volume 26, Issue 3, Pages 231-237	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/7632	-
dc.description.abstract	In this article, using the Mizar system [1], [2], we discuss the continuity of bounded linear operators on normed linear spaces. In the first section, it is discussed that bounded linear operators on normed linear spaces are uniformly continuous and Lipschitz continuous. Especially, a bounded linear operator on the dense subset of a complete normed linear space has a unique natural extension over the whole space. In the next section, several basic currying properties are formalized.In the last section, we formalized that continuity of bilinear operator is equivalent to both Lipschitz continuity and local continuity. We referred to [4], [13], and [3] in this formalization.	-
dc.description.sponsorship	This study was supported in part by JSPS KAKENHI Grant Number JP17K00182.	-
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	Lipschitz continuity	-
dc.subject	uniform continuity	-
dc.subject	bounded linear operators	-
dc.subject	bilinear operators	-
dc.title	Continuity of Bounded Linear Operators on Normed Linear Spaces	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2018-0021	-
dc.description.Affiliation	Kazuhisa Nakasho - Yamaguchi University, Yamaguchi, Japan	-
dc.description.Affiliation	Yuichi Futa - Tokyo University of Technology, Tokyo, 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.identifier.eissn	1898-9934	-
dc.description.volume	26	-
dc.description.issue	3	-
dc.description.firstpage	231	-
dc.description.lastpage	237	-
dc.identifier.citation2	Formalized Mathematics	-
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