On the submultiplicativity and subadditivity of the spectral and essential spectral radius

This note aims to correct a too strong generalization in the proof of Proposition 1. In the initially published version of this article, the proof of Proposition 1 incorrectly stated that the spectral radius of a sum of two general square matrices, W 1 and W 2 , is bounded by the maximum of the spectral radii of each matrix. Nevertheless, this statement does not hold in general for any type of square matrix, which means that there can be cases in which the inequality in the published proof does not hold. For a general stationarity condition, we can rely on the findings of Kheifets and Saikkonen (2020), which lead to the following proposition.

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On the submultiplicativity and subadditivity of the spectral and essential spectral radius

Abstract: Suppose that A and B are positive operators on an ordered Banach space with a normal and generating cone satisfying 0 ≤ AB ≤ BA.

Cited by 2 publications

References 22 publications

A Smooth Transition Autoregressive Model for Matrix-Variate Time Series

A Smooth Transition Autoregressive Model for Matrix-Variate Time Series

Correction to: A Smooth Transition Autoregressive Model for Matrix-Variate Time Series

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