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W. Auzinger, G. Kirlinger:
"Kreiss resolvent conditions and strengthened Cauchy-Schwarz inequalities";
Applied Numerical Mathematics, 18 (1995), S. 57 - 67.

In the present paper it is shown how the resolvent conditions in the Kreiss Matrix Theorem for e^{tA} and A^\nu, respectively, can be reformulated as certain Strengthened Cauchy-Schwarz Inequalities (SCSIs) to be satisfied for all pairs w, Aw (w \in \C^n).This yields certain generalizations of the notions `logarithmic norm' and `numerical radius', respectively.

http://dx.doi.org/10.1016/0168-9274(95)00043-T

http://www.math.tuwien.ac.at/~winfried/papers/rc.pdf