Riesz Representation Theorem on Bilinear Spaces of Truncated Laurent Series

Sabarinsyah Sabarinsyah, Hanni Garminia, Pudji Astuti

Abstract


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.

Keywords


bilinear forms; closed subspaces; non-degenerate; Riesz representation theorem; truncated Laurent series.

Full Text:

(PDF)

References


Fuhrmann, P.A., Duality in Polynomial Models with some Applications to Geometric Control Theory, IEEE Transaction on Automatic Control, 26(1), pp. 284-295, 1981.

Fuhrmann, P.A., A Study of Behaviors, Linear Algebra and its Appl., 351-352, pp. 303-380, 2002.

Roman, S., Advanced Linear Algebra, Springer-Verlag New York, 2007.




DOI: http://dx.doi.org/10.5614%2Fj.math.fund.sci.2017.49.1.3

Refbacks

  • There are currently no refbacks.


View my Stats

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.