AN INVESTIGATION ON THE BEHAVIOUR OF UNBOUNDED OPERATORS IN Г-HILBERT SPACE

Year 2021, Volume: 3 Issue: 2, 1 - 8, 10.10.2021

Sahın Injamamul Islam

https://doi.org/10.54286/ikjm.923786

Abstract

In this paper, we investigate about the behavior of unbounded operators in Г-Hilbert Space. Here we discussed about the adjoint, self-adjoint, symmetric and other related properties of densely defined operator. We proof some related theorems and corollaries and will show the characterizations of this operators in Г -Hilbert Space.

Keywords

Gamma-Hilbert Space, Closed operator, Densely defined operator, self-adjoint of densely defined operator, symmetric of densely defined operator

References

• Reference1 [1]A. Ghosh,A. Das and T.E. Aman(2017) Representation Theorem on Г-Hilbert Space,International Journal of Mathematics Trends and Technology,52(9):608-615.
• Reference2 [2] B.K. Lahiri, 1982.Elements Of Functional Analysis. The World Press Private Limited,Kolkata.
• Reference3 [3] B V Limaye .2013, second Edition ,FUNCTIONAL ANALYSIS,New age International (p)Limited,Publishers,Delhi,India.
• Reference4 [4] E.Kreyszig, 1978. Introductory Functional Analysis with applications, john wiley and sons.
• Reference5 [5] Garayev, M. T., Gürdal, M., & Saltan, S. (2017). Hardy type inequality for reproducing kernel Hilbert space operators and related problems. Positivity, 21(4), 1615-1623.
• Reference6 [6] Islam, S . (2020). On Some bounded Operators and their characterizations in Г-Hilbert Space. Cumhuriyet Science Journal, 41 (4) , 854-861 . DOI: 10.17776/csj.747393.
• Reference7 [7] John B. Conway .1996, A Course in Functional Analysis. Springer –Verlag New York, INC,USA.
• Reference8 [8] L.Debnath, Piotr Mikusinski, 1980. Introduction to Hilbert Space with applications, Academic Press,INC.New York,Toronto.
• Reference9 [9] T.E.Aman and D.K.Bhttacharya(2003). Г-Hilbert Space and linear quadratic control problem. Rev.Acad.Canr.Cienc; xv (Nums. 1-2),107-114 (publicado en Julio de 2004) .