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An Extension of Polyak’s Theorem in a Hilbert Space

✍ Scribed by A. Baccari; B. Samet


Publisher
Springer
Year
2008
Tongue
English
Weight
301 KB
Volume
140
Category
Article
ISSN
0022-3239

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Rolle's Theorem for Polynomials of Degre
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In an infinite-dimensional real Hilbert space, we introduce a class of fourthdegree polynomials which do not satisfy Rolle's Theorem in the unit ball. Extending what happens in the finite-dimensional case, we show that every fourth-degree polynomial defined by a compact operator satisfies Rolle's Th