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Algebra i Analiz, 2013, Volume 25, Issue 3, Pages 3–51 (Mi aa1336)  
This article is cited in 6 scientific papers (total in 6 papers)

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Sublinear dimension growth in the Kreiss Matrix Theorem

N. Nikolskiab

a University Bordeaux 1, France
b St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka, 27, 191023, St. Petersburg, Russia
Full-text PDF (522 kB) Citations (6)
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Abstract: We discuss a possible sublinear dimension growth in the Kreiss Matrix Theorem bounding the stability constant in terms of the Kreiss resolvent characteristic. 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 we use and compare the approaches by C. A. McCarthy–J. Schwartz (1965) and V. I. Gurarii–N. I. Gurarii (1971). The sharpness issue is verified via finite Muckenhoupt bases (by using mostly the approach by M. Spijker, S. Tracogna, and B. Welfert (2003)).
Keywords: power bounded, Kreiss Matrix Theorem, unconditional basis, Muckenhoupt condition.
Received: 12.12.2012
English version:
St. Petersburg Mathematical Journal, 2014, Volume 25, Issue 3, Pages 361–396
DOI: https://doi.org/10.1090/S1061-0022-2014-01295-2
Bibliographic databases:
Document Type: Article
Language: English
Citation: N. Nikolski, “Sublinear dimension growth in the Kreiss Matrix Theorem”, Algebra i Analiz, 25:3 (2013), 3–51; St. Petersburg Math. J., 25:3 (2014), 361–396
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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