<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The main aim of this article is proving properties of bilinear operators on normed linear spaces formalized by means of Mizar [1]. In the first two chapters, algebraic structures [3] of bilinear operators on linear spaces are discussed. Especially, the space of bounded bilinear operators on normed linear spaces is developed here. In the third chapter, it is remarked that the algebraic structure of bounded bilinear operators to a certain Banach space also constitutes a Banach space.</p><p>In the last chapter, the correspondence between the space of bilinear operators and the space of composition of linear opearators is shown. We referred to [4], [11], [2], [7] and [8] in this formalization.</p></abstract>

The main aim of this article is proving properties of bilinear operators on normed linear spaces formalized by means of Mizar [1]. In the first two chapters, algebraic structures [3] of bilinear operators on linear spaces are discussed. Especially, the space of bounded bilinear operators on normed linear spaces is developed here. In the third chapter, it is remarked that the algebraic structure of bounded bilinear operators to a certain Banach space also constitutes a Banach space.In the last chapter, the correspondence between the space of bilinear operators and the space of composition of linear opearators is shown. We referred to [4], [11], [2], [7] and [8] in this formalization.

Bilinear Operators on Normed Linear Spaces

Formalized Mathematics

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{"article-title":"Bilinear Operators on Normed Linear Spaces"}

The main aim of this article is proving properties of bilinear operators on normed linear spaces formalized by means of Mizar [1]. In the first two chapters,...

Bilinear Operators on Normed Linear Spaces

Publicado en línea: 16 may 2019

Páginas: 15 - 23

Aceptado: 27 feb 2019

DOI: https://doi.org/10.2478/forma-2019-0002

Palabras clave
Lipschitz continuity, bounded linear operator, bilinear operator, algebraic structure, Banach space

© 2019 Kazuhisa Nakasho, published by Sciendo

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

Bilinear Operators on Normed Linear Spaces

Publicado en línea: 16 may 2019

Páginas: 15 - 23

Aceptado: 27 feb 2019

DOI: https://doi.org/10.2478/forma-2019-0002

Palabras claveLipschitz continuity, bounded linear operator, bilinear operator, algebraic structure, Banach space

© 2019 Kazuhisa Nakasho, published by Sciendo

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

Palabras clave
Lipschitz continuity, bounded linear operator, bilinear operator, algebraic structure, Banach space