Finiteness Property of a Bounded Set of Matrices with Uniformly Sub-Peripheral Spectrum

Details Finiteness Property of a Bounded Set of Matrices with Uniformly Sub-Peripheral Spectrum Finiteness Property of a Bounded Set of Matrices with Uniformly Sub-Peripheral Spectrum

2011-06-12

arxiv.org/abs/1106.2298v3

Journal of Communications Technology and Electronics, 2011, Vol. 56, No. 12, pp. 1564-1569

Mathematics

Functional Analysis

8 pages, 29 bibliography references. Minor changes in v3

Scientific paper

10.1134/S1064226911120096

In the paper, a simple condition guaranteing the finiteness property for a bounded set of matrices is presented. Given a bounded set S of real or complex matrices, it is shown that existence of a sequence of matrix products such that the spectrum of each matrix in this sequence is uniformly sub-peripheral and tends to the joint spectral radius of S, guarantees the spectral finiteness property for S.

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