TY  - JOUR
T1  - Spectral Theorem for Compact Self -Adjoint Operator in Γ -Hilbert space
AU  - Islam, Sahın Injamamul
AU  - Sarkar, Nırmal
AU  - Das, Ashoke
PY  - 2022
DA  - March
DO  - 10.31197/atnaa.877757
JF  - Advances in the Theory of Nonlinear Analysis and its Application
JO  - ATNAA
PB  - Erdal KARAPINAR
WT  - DergiPark
SN  - 2587-2648
SP  - 93
EP  - 100
VL  - 6
IS  - 1
LA  - en
AB  - In this article we investigate some basic results of Self-adjoint Operator in Γ-Hilbert space. We proof some similar results on Self-adjoint Operator in this space with some specific norm. Finally we will prove that the Spectral Theorem for Compact Self-adjoint Operator in Γ -Hilbert space and the converse is true.
KW  - Compact operator
KW  - 
KW  - Self-adjoint Operator
KW  - 
KW  - Spectral Theorem
KW  - 
KW  - Γ-Hilbert Space
CR  - [1] T.E. Aman, D.K. Bhattacharya, Γ-Hilbert Space and linear quadratic control problem, Rev. Acad. Canar. Cienc,
XV(Nums. 1-2), (2003), 107-114.
CR  - [2] A. Ghosh, A. Das, T.E. Aman, Representation Theorem on Γ-Hilbert Space, International Journal of Mathematics Trends
and Technology (IJMTT), V52(9), December (2017), 608-615.
CR  - [3] S. Islam, On Some bounded Operators and their characterizations in Γ-Hilbert Space, Cumhuriyet Science Journal, 41 (4)
(2020), 854-861.
CR  - [4] J.B. Conway, A Course in Functional Analysis, 2nd ed., USA: Springer, (1990), 26-60.
CR  - [5] L. Debnath, P. Mikusinski, Introduction to Hilbert Space with applications, 3rd ed, USA: Elsevier, (2005), 145-210.
CR  - [6] B.V. Limaye, Functional Analysis, 2nd ed., Delhi New age International(p) Limited, (1996).
CR  - [7] B.K. Lahiri, Elements Of Functional Analysis, 5th ed, Calcutta, The World Press, (2000).
UR  - https://doi.org/10.31197/atnaa.877757
L1  - https://dergipark.org.tr/tr/download/article-file/1567862
ER  -