## Vector norm inequalities for power series of operators in Hilbert spaces.(English)Zbl 1320.47013

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.

### MSC:

 47A63 Linear operator inequalities
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