Riesz Representation Theorem on Bilinear Spaces of Truncated Laurent Series
DOI:
https://doi.org/10.5614/j.math.fund.sci.2017.49.1.3Keywords:
bilinear forms, closed subspaces, non-degenerate, Riesz representation theorem, truncated Laurent series.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.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.
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Published
2017-04-06
How to Cite
Sabarinsyah, S., Garminia, H., & Astuti, P. (2017). Riesz Representation Theorem on Bilinear Spaces of Truncated Laurent Series. Journal of Mathematical and Fundamental Sciences, 49(1), 33-39. https://doi.org/10.5614/j.math.fund.sci.2017.49.1.3
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