Riesz Representation Theorem on Bilinear Spaces of Truncated Laurent Series

Sabarinsyah Sabarinsyah (Algebra Research Division, Faculty of Mathematics and Natural Sciences , Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132)
Hanni Garminia (Algebra Research Division, Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung, Bandung 40132)
Pudji Astuti (Algebra Research Division, Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung, Bandung 40132)

Journal of Mathematical and Fundamental Sciences
Vol. 49 No. 1 (2017)

In this study a generalization of the Riesz representation theorem on non-degenerate bilinear spaces, particularly on spaces of truncated Laurent series, was developed. It was shown that any linear functional on a non-degenerate bilinear space is representable by a unique element of the space if and only if its kernel is closed. Moreover an explicit equivalent condition can be identified for the closedness property of the kernel when the bilinear space is a space of truncated Laurent series.