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http://hdl.handle.net/11320/7840
Tytuł: | Continuity of Multilinear Operator on Normed Linear Spaces |
Autorzy: | Nakasho, Kazuhisa Shidama, Yasunari |
Słowa kluczowe: | Lipschitz continuity bounded linear operators multilinear operators Banach space |
Data wydania: | 2019 |
Data dodania: | 21-maj-2019 |
Wydawca: | DeGruyter Open |
Źródło: | Formalized Mathematics, Volume 27, Issue 1, Pages 61-65 |
Abstrakt: | 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. |
Afiliacja: | Kazuhisa Nakasho - Yamaguchi University, Yamaguchi, Japan Yasunari Shidama - Shinshu University, Nagano, Japan |
URI: | http://hdl.handle.net/11320/7840 |
DOI: | 10.2478/forma-2019-0006 |
ISSN: | 1426-2630 |
e-ISSN: | 1898-9934 |
metadata.dc.identifier.orcid: | 0000-0003-1110-4342 |
Typ Dokumentu: | Article |
Występuje w kolekcji(ach): | Formalized Mathematics, 2019, Volume 27, Issue 1 |
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