Sublinear dimension growth in the Kreiss Matrix Theorem

Nikolski, N.

doi:10.1090/S1061-0022-2014-01295-2

Sublinear dimension growth in the Kreiss Matrix Theorem
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by N. Nikolski

St. Petersburg Math. J. 25 (2014), 361-396

DOI: https://doi.org/10.1090/S1061-0022-2014-01295-2

Published electronically: May 16, 2014

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Abstract:

A possible sublinear dimension growth in the Kreiss Matrix Theorem, bounding the stability constant in terms of the Kreiss resolvent characteristic, is discussed. Such a growth is proved for matrices having unimodular spectrum and acting on a uniformly convex Banach space. The principal ingredients to results obtained come from geometric properties of eigenvectors, where the approaches by C. A. McCarthy–J. Schwartz (1965) and V. I. Gurarii–N. I. Gurarii (1971) are used and compared. The sharpness issue is verified via finite Muckenhoupt bases (by using mostly the approach by M. Spijker, S. Tracogna, and B. Welfert (2003)).

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