The main aim of this article is proving properties of bilinear operators on normed linear spaces formalized by means of Mizar . In the first two chapters, algebraic structures  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 , , ,  and  in this formalization.
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 Grzegorz Bancerek Czesław Byliński Adam Grabowski Artur Korniłowicz Roman Matuszewski Adam Naumowicz and Karol Pak. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning 61(1):9–32 2018. doi:10.1007/s10817-017-9440-6.
 Nelson Dunford and Jacob T. Schwartz. Linear operators I. Interscience Publ. 1958.
 Adam Grabowski Artur Korniłowicz and Christoph Schwarzweller. On algebraic hierarchies in mathematical repository of Mizar. In M. Ganzha L. Maciaszek and M. Paprzycki editors Proceedings of the 2016 Federated Conference on Computer Science and Information Systems (FedCSIS) volume 8 of Annals of Computer Science and Information Systems pages 363–371 2016. doi:10.15439/2016F520.