Abstract Let A be a nonzero positive operator on a complex Hilbert space (ℋ, 〈 ⋅, ⋅ 〉) (H, \, \, , \, ), inducing the semi-inner product 〈 x, y 〉 A: = 〈 A x, y 〉 x, y₀: = Ax, y for x, y ∈ ℋ x, y. The space (ℋ, ∥ ⋅ ∥ A) (H, \|\|₀), where ∥ x ∥ A = 〈 x, x 〉 A \|x\|₀= x, x₀, is a semi-Hilbert space equipped with a seminorm induced by 〈 ⋅, ⋅ 〉 A \, \, , \, ₀. In this paper, we establish the inequality | ∑ i = 1 n c i 〈 x, y i 〉
Aljawi et al. (Thu,) studied this question.
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