<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the first chapter, the notion of multilinear operator on real linear spaces is discussed. The algebraic structure [2] of multilinear operators is introduced here. In the second chapter, the results of the first chapter are extended to the case of the normed spaces. This chapter shows that bounded multilinear operators on normed linear spaces constitute the algebraic structure. We referred to [3], [7], [5], [6] in this formalization.</p></abstract>

In the first chapter, the notion of multilinear operator on real linear spaces is discussed. The algebraic structure [2] of multilinear operators is introduced here. In the second chapter, the results of the first chapter are extended to the case of the normed spaces. This chapter shows that bounded multilinear operators on normed linear spaces constitute the algebraic structure. We referred to [3], [7], [5], [6] in this formalization.

Multilinear Operator and Its Basic Properties

Formalized Mathematics

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

{"article-title":"Multilinear Operator and Its Basic Properties"}

In the first chapter, the notion of multilinear operator on real linear spaces is discussed. The algebraic structure [2] of multilinear operators is introduced...

Multilinear Operator and Its Basic Properties

Publié en ligne: 16 mai 2019

Pages: 35 - 45

Accepté: 27 févr. 2019

DOI: https://doi.org/10.2478/forma-2019-0004

Mots clés
Lipschitz continuity, bounded linear operators, bilinear operators, algebraic structure, Banach space

© 2019 Kazuhisa Nakasho, published by Sciendo

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

Multilinear Operator and Its Basic Properties

Publié en ligne: 16 mai 2019

Pages: 35 - 45

Accepté: 27 févr. 2019

DOI: https://doi.org/10.2478/forma-2019-0004

Mots clésLipschitz continuity, bounded linear operators, bilinear operators, algebraic structure, Banach space

© 2019 Kazuhisa Nakasho, published by Sciendo

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

Mots clés
Lipschitz continuity, bounded linear operators, bilinear operators, algebraic structure, Banach space