Representation Theorem on Γ-Hilbert Space

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

“…then it is easy to prove that x γ satisfy all the conditions of norm. The author in [2] has all ready proved the following results.…”

“…Further development of this literature was found in 2017 by A. Ghosh, A. Das, and T.E. Aman in their paper [2]. They dened γ-orthogonality, proved the Unique decomposition theorem and Representation theorem in Γ-Hilbert space.…”

“…Denition 2.3. [2] Let x, y ∈ H Γ , then x, y are γ-orthogonal if and only if x, γ, y = 0. In symbol we write…”

An Investigation on the Behaviour of Unbounded Operators in Г-Hilbert Space

“…Г-Hilbert space plays an important role in generalization of general linear quadratic control problems in an abstract space [1] which was motivated from the work of L.Debnath and Pitor Mikusinski [8] but there not enough literature found to study about the unbounded operators in Г-Hilbert space. The definition of Г-Hilbert space was introduced by Bhattacharya D.K.…”

“…Further development was made in 2017 by A.Ghosh, A.Das and T.E. Aman in their research paper [1]. In [6] S.Islam and A.Das discussed about the properties of bounded operators in Г-Hilbert Space.…”