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Kreiss resolvent conditions and strengthened Cauchy-Schwarz inequalities. (English) Zbl 0834.15020

It is shown how the resolvent conditions in the Kreiss matrix theorem [see H.-O. Kreiss, BIT 2, 153-181 (1962; Zbl 0109.347)] for \(e^{tA}\) and \(A^\nu\), respectively, can be reformulated as certain strengthened Cauchy-Schwarz inequalities to be satisfied for all pairs \(w\), \(Aw\) \((w\in \mathbb{C}^n)\). This yields certain generalizations of the notions “logarithmic norm” and “numerical radius”, respectively.

MSC:

15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory

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References:

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