Continuous-Like Linear Operators on Bilinear Spaces

Sabarinsyah Sabarinsyah (Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Ganesha No. 10 Bandung 40132)
Hanni Garminia (Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Ganesha No. 10 Bandung 40132)
Pudji Astuti (Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Ganesha No. 10 Bandung 40132)

Journal of Mathematical and Fundamental Sciences
Vol. 52 No. 2 (2020)

This paper introduces continuous-like linear operators on bilinear spaces as a generalization of continuous linear operators on Hilbert spaces. It is well known that the existence of the adjoint of a linear operator on a Hilbert space is equivalent to the operator being continuous. In this paper, this result is extended to the class of linear operators on bilinear spaces. It is shown that the existence of the adjoint of a linear operator on a bilinear space is guaranteed if and only if the operator is continuous-like.