Sentence examples for linear bounded operator on the from inspiring English sources

Assume that B is a strongly positive linear bounded operator on the Hilbert space H with a coefficient γ ¯ > 0 and 0 < ϱ < ∥ B ∥ − 1.

Let be a strongly positive linear bounded operator on : that is, there is a constant with property (1.6).

Assume B is a strong positive linear bounded operator on a Hilbert space H with the coefficient γ ¯ > 0 and 0 < ρ ≤ ∥ B ∥ − 1.

Assume A is a strongly positive linear bounded operator on a Hilbert space H with the coefficient γ ¯ > 0 and 0 < ρ ≤ ∥ A ∥ − 1, then ∥ I − ρ A ∥ ≤ 1 − ρ γ ¯.

Let A be a strongly positive linear bounded operator on H if there is a constant γ ¯ > 0 with the property 〈 A x, x 〉 ≥ γ ¯ ∥ x ∥ 2, ∀ x ∈ H.

where is a strongly positive linear bounded operator on, is a contraction on and.

Assume is a strongly positive linear bounded operator on a Hilbert space with coefficient and.

Assume that is a strong positive linear bounded operator on a Hilbert space with coefficient and.

Let be a strongly positive linear bounded operator on with coefficient and.

Assume is a strongly monotone linear bounded operator on a Hilbert space with coefficient.

Since is a linear bounded operator on, by (1.27), we have (3.14).