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.
Downloads
Download data is not yet available.
References
Bartle. R.G, Sherbert D.R (2000), Introduction to Real Analysis, Third Edition. John Wiley and Sons, Inc, USA
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
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.
Section
Articles
Authors who publish with this Journal agree to the following terms:
- Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
- Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.
