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)).References
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Bibliographic Information
- N. Nikolski
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia; University Bordeaux 1, France
- Email: Nikolai.Nikolski@math.u-bordeaux1.fr
- Received by editor(s): December 12, 2012
- Published electronically: May 16, 2014
- © Copyright 2014 American Mathematical Society
- Journal: St. Petersburg Math. J. 25 (2014), 361-396
- MSC (2010): Primary 47A10
- DOI: https://doi.org/10.1090/S1061-0022-2014-01295-2
- MathSciNet review: 3184597
Dedicated: To Boris Mikhaĭlovich Makarov on his 80th anniversary — gratefully remembering unforgettable lessons in Analysis around 1960