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Differentiators and the geometry of polynomials

✍ Scribed by Rajesh Pereira

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
135 KB
Volume
285
Category
Article
ISSN
0022-247X

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✦ Synopsis

In 1959, Davis introduced the concept of a differentiator of an operator on a finite-dimensional Hilbert space. We prove that every such operator possesses a differentiator. We also use the theory of differentiators to solve several problems in the geometry of polynomials. For instance, we answer in the affirmative a twenty year old unsolved conjecture of Schoenberg, a related conjecture of Katsoprinakis and a fifty year old unsolved conjecture of De Bruijn and Springer.

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## Abstract We show that the symmetric injective tensor product space is not complex strictly convex if __E__ is a complex Banach space of dim __E__ β‰₯ 2 and if __n__ β‰₯ 2 holds. It is also reproved that β„“~∞~ is finitely represented in if __E__ is infinite‐dimensional and if __n__ β‰₯ 2 holds, which