Vector norm inequalities for power series of operators in Hilbert spaces

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In this paper, vector norm inequalities that provides upper bounds for the Lipschitz quantity ║f (T) x - f (V ) x ║ for power series f(z) = ∑n=0 anzn; bounded linear operators T; V on the Hilbert space H and vectors x ∈ H are established. Applications in relation to Hermite- Hadamard type inequalities and examples for elementary functions of interest are given as well.

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