Continuous-Like Linear Operators on Bilinear Spaces

• Main Authors: Sabarinsyah Sabarinsyah, Hanni Garminia, Pudji Astuti
• Format: Article
• Language: English
• Published: ITB Journal Publisher 2020-09-01
• Series: Journal of Mathematical and Fundamental Sciences
• Subjects: adjoint operators; bilinear spaces; closed subspaces; continuous; continuous-like; Hilbert spaces
• Online Access: https://journals.itb.ac.id/index.php/jmfs/article/view/10246

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.