<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p><p>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.</p></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.

Continuity of Multilinear Operator on Normed Linear Spaces

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License.

{"article-title":"Continuity of Multilinear Operator on Normed Linear Spaces"}

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...

Continuity of Multilinear Operator on Normed Linear Spaces

Online veröffentlicht: 16. Mai 2019

Seitenbereich: 61 - 65

Akzeptiert: 27. Feb. 2019

DOI: https://doi.org/10.2478/forma-2019-0006

Schlüsselwörter
Lipschitz continuity, bounded linear operators, multilinear operators, Banach space

© 2019 Kazuhisa Nakasho et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License.

Continuity of Multilinear Operator on Normed Linear Spaces

Online veröffentlicht: 16. Mai 2019

Seitenbereich: 61 - 65

Akzeptiert: 27. Feb. 2019

DOI: https://doi.org/10.2478/forma-2019-0006

SchlüsselwörterLipschitz continuity, bounded linear operators, multilinear operators, Banach space

© 2019 Kazuhisa Nakasho et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License.

Schlüsselwörter
Lipschitz continuity, bounded linear operators, multilinear operators, Banach space