Contraction And 𝐂(𝛂)- Suboperator Classes

In this paper we characterize the generalisation of contraction in Hilbert space and 𝐶(𝛼)- Suboperator class and establish some new result in the class of 𝐶(𝛼)- Suboperator [1] and its contractive extensions of a 𝐶(𝛼)- Suboperator class in a complex Hilbert space. The characterizations include a quadratic form inequality. The bounded linear operator 𝑇 in complex Hilbert space which satisfy 𝑇 = 𝛽𝐼 +(1 −𝛽)𝑈 where 𝛽 ∈ (0,1) and 𝑈 is a contraction (‖𝑈‖ ≤ 1)