On some aspects of spectral theory for infinite bounded non-negative matrices in max algebra

TL;DR

This paper explores spectral properties of infinite bounded nonnegative matrices in max algebra, deriving formulas, Perron-Frobenius type results, and continuity properties, with implications for matrix block structures.

Contribution

It introduces new spectral radius formulas and Perron-Frobenius type theorems specifically for infinite matrices in max algebra, extending classical matrix theory.

Findings

Derived spectral radius formulas for infinite matrices

Proved Perron-Frobenius type results in max algebra

Established continuity properties of spectral characteristics

Abstract

Several spectral radii formulas for infinite bounded nonnegative matrices in max algebra are obtained. We also prove some Perron-Frobenius type results for such matrices. In particular, we obtain results on block triangular forms, which are similar to results on Frobenius normal form of $n \times n$ matrices. Some continuity results are also established.