Vector norm inequalities for power series of operators in Hilbert spaces (Q488483)

Vector norm inequalities for power series of operators in Hilbert spaces are highlighted. The authors deal with vector norm inequalities that provide upper bounds for the Lipschitz quantity \(\|f(T)x-f(V)x\|\) for power series \(f(z)= \sum^{\infty}_{n = 0} a_{n}z^{n}\), bounded linear operators \(T, V\) on the Hilbert space \(H\), and vectors \(x\in H \). Earlier works on Hermite-Hadamard type inequalities are discussed. Appropriate applications and examples for elementary functions of interest are mentioned.