Representation Theorem on Γ-Hilbert Space

Amit Ghosh; Ashoke Das; Towhid E Aman

doi:https://doi.org/10.14445/22315373/IJMTT-V52P587

International Journal of Mathematics Trends and Technology

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Volume 52 | Number 9 | Year 2017 | Article Id. IJMTT-V52P587 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P587

Representation Theorem on Γ-Hilbert Space

Amit Ghosh, Ashoke Das, Towhid E Aman

Abstract

In this paper we discuss about the simple properties of Γ-Hilbert space, introduced by D.K.Bhattacharya and T.E.Aman in their paper Γ-Hilbert Space and linear Quadratic Control problem in 2003. We have defined the orthogonality in Γ-Hilbert space and discuss about the closest point property, Unique Decomposition Theorem following the defined orthogonality on that space . Further we discuss the representation of any bounded linear functionals on Γ-Hilbert space in terms of inner product in that space.

Keywords

Hilbert space, Γ-Hilbert Space , Unique Decomposition Theorem , Riesz Representation Theorem.

References

[1] T.E.Aman and D.K.Bhattacharya :Γ-Hilbert space and linear quadratic control problem. Rev. Acad. Canr. Cienc; xv (Nums. 1-2), 107-114 (2003).
[2] L.Debnath , P.Mikusi~nski, 1980,Introduction to Hilbert Space with applications,Academic Press, INC,New York, Toronto.
[3] B.K.Lahiri, 1982. Elements Of Functional Analysis. The World Press Private Limited, Kolkata.
[4] E.Kreyszig,1978.Introductory Functional Analysis with applications, John Wiley and sons.

Citation :

Amit Ghosh, Ashoke Das, Towhid E Aman, "Representation Theorem on Γ-Hilbert Space," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 9, pp. 608-615, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P587