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Spectral Theorem for Compact Self -Adjoint Operator in Γ -Hilbert space

Year 2022, Volume: 6 Issue: 1, 93 - 100, 31.03.2022

Nırmal Sarkar Sahın Injamamul Islam Ashoke Das

https://doi.org/10.31197/atnaa.877757

Abstract

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.

Keywords

Compact operator, Self-adjoint Operator, Spectral Theorem, Γ-Hilbert Space

References

  • [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.
  • [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.
  • [3] S. Islam, On Some bounded Operators and their characterizations in Γ-Hilbert Space, Cumhuriyet Science Journal, 41 (4) (2020), 854-861.
  • [4] J.B. Conway, A Course in Functional Analysis, 2nd ed., USA: Springer, (1990), 26-60.
  • [5] L. Debnath, P. Mikusinski, Introduction to Hilbert Space with applications, 3rd ed, USA: Elsevier, (2005), 145-210.
  • [6] B.V. Limaye, Functional Analysis, 2nd ed., Delhi New age International(p) Limited, (1996).
  • [7] B.K. Lahiri, Elements Of Functional Analysis, 5th ed, Calcutta, The World Press, (2000).

Year 2022, Volume: 6 Issue: 1, 93 - 100, 31.03.2022

Nırmal Sarkar Sahın Injamamul Islam Ashoke Das

https://doi.org/10.31197/atnaa.877757

Abstract

References

  • [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.
  • [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.
  • [3] S. Islam, On Some bounded Operators and their characterizations in Γ-Hilbert Space, Cumhuriyet Science Journal, 41 (4) (2020), 854-861.
  • [4] J.B. Conway, A Course in Functional Analysis, 2nd ed., USA: Springer, (1990), 26-60.
  • [5] L. Debnath, P. Mikusinski, Introduction to Hilbert Space with applications, 3rd ed, USA: Elsevier, (2005), 145-210.
  • [6] B.V. Limaye, Functional Analysis, 2nd ed., Delhi New age International(p) Limited, (1996).
  • [7] B.K. Lahiri, Elements Of Functional Analysis, 5th ed, Calcutta, The World Press, (2000).
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Nırmal Sarkar 0000-0002-9050-1479

Sahın Injamamul Islam 0000-0002-8587-7922

Ashoke Das 0000-0002-6612-0182

Publication Date March 31, 2022
Published in Issue Year 2022 Volume: 6 Issue: 1

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