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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Sublinear dimension growth in the Kreiss Matrix Theorem

Author: N. Nikolski
Original publication: Algebra i Analiz, tom 25 (2013), nomer 3.
Journal: St. Petersburg Math. J. 25 (2014), 361-396
MSC (2010): Primary 47A10
Published electronically: May 16, 2014
MathSciNet review: 3184597
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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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Additional Information

N. Nikolski
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia; University Bordeaux 1, France

Keywords: Power bounded, Kreiss Matrix Theorem, unconditional basis, Muckenhoupt condition
Received by editor(s): December 12, 2012
Published electronically: May 16, 2014
Dedicated: To Boris Mikhaĭlovich Makarov on his 80th anniversary — gratefully remembering unforgettable lessons in Analysis around 1960
Article copyright: © Copyright 2014 American Mathematical Society

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