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Rolle’s theorem for polynomials of degree four in a Hilbert space. (English) Zbl 1086.46032
Summary: In an infinite-dimensional real Hilbert space, we introduce a class of fourth-degree 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 theorem.

MSC:
46G05 Derivatives of functions in infinite-dimensional spaces
46G25 (Spaces of) multilinear mappings, polynomials
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