TEOREMA REPRESENTASI RIESZ–FRECHET PADA RUANG HILBERT
Keywords:
Banach Spaces, Hilbert Spaces, Norm Space, Pre-Hilbert Spaces, Representation Riesz
Abstract
Hilbert space is a very important idea of the Davids Hilbert invention. In 1907, Riesz and Fréchet developed one of the theorem in Hilbert space called the Riesz-Fréchet representation
theorem. This research contains some supporting definitions Banach space, pre-Hilbert spaces, Hilbert spaces, the duality of Banach and Riesz-Fréchet representation theorem. On Riesz-
Fréchet representation theorem will be shown that a continuous linear functional that exist in the Hilbert space is an inner product, in other words, there is no continuous linear functional on a Hilbert space except the inner product.
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References
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Zeidler. E (1995). Applied Functional Analysis, Springer-Verlag, Inc, New York
Conway. J. B. A (1989). Course in Functional Analysis, Second Edition. Springer-Verlag, New York
Devito. C. L (1990). Functional Analysis and Linear Operator Theory. Addison-Wesley publishing Company, New York
Halmos. P. R (1957), Introduction to Hilbert Space and the Theory of Spectral Multiplicity. Second edition, Chelsea, New York
Howard. A (1987). Aljabar Linear Elementer. Erlangga, Jakarta
Kreyszig. E (1978). Introduction Functional Analysis Aplications. John Wiley& Son, New York
Leon, Steven. J (2001). Aljabar Linear dan Aplikasinya. Erlangga, Jakarta
Maddox. I. J (1970). Element of Funcional Analysis. Cambridge Univ. Press, London
Royden. H. L (1989). Real Analysis (third Edition). Macmillan Publishing Company, New York
Rudin, W (1973). Functional Analysis . Second edition. McGraw-Hill, Inc, United State
Zaanen. A. C (1997). Introduction to Operator Theory in Riesz Spaces. Springer-Verlag, New York
Zeidler. E (1995). Applied Functional Analysis, Springer-Verlag, Inc, New York
Published
2011-12-01
How to Cite
[1]
M. Talakua and S. Nanuru, “TEOREMA REPRESENTASI RIESZ–FRECHET PADA RUANG HILBERT”, BAREKENG: J. Math. & App., vol. 5, no. 2, pp. 1-8, Dec. 2011.
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