Abstract
In this article we study the structure of the space of polynomials of degree n, considered as a finite-dimensional Banach space. We give some estimates of the Banach-Mazur distance of this space and its subspaces to the classical Banach spaces l p (m). In the case when the degree of the polynomials is 2n we show that the space can be decomposed as the direct sum of n subspaces each of which is isometric to a finite dimensional ℓ∞ space.
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© 1987 Springer-Verlag
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Shekhtman, B. (1987). On the geometry of real polynomials. In: Saff, E.B. (eds) Approximation Theory, Tampa. Lecture Notes in Mathematics, vol 1287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078904
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DOI: https://doi.org/10.1007/BFb0078904
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Print ISBN: 978-3-540-18500-0
Online ISBN: 978-3-540-47991-8
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