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Bilinear Operators on Normed Linear Spaces

2019; De Gruyter Open; Volume: 27; Issue: 1 Linguagem: Inglês

10.2478/forma-2019-0002

1898-9934

Kazuhisa Nakasho,

Cryptography and Data Security

Summary 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.