Rolle's Theorem for Polynomials of Degree Four in a Hilbert Space |
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| Authors: | Jesús Ferrer |
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| Institution: | Departamento de Análisis Matemático, Universidad de Valencia, Dr. Moliner 50, 46100 Burjasot, Valencia, Spainf1jesus.ferrer@uv.esf1 |
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| Abstract: | 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. |
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| Keywords: | Rolle's Theorem Hilbert spaces polynomials |
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