Geodesic
Spectraloid operator polynomials, the approximate numerical range and an Eneström–Kakeya theorem in Hilbert space
Jan Swoboda 1   ; Harald K. Wimmer 2
1 Max-Planck-Institut für Mathematik D-53111 Bonn, Germany
2 Mathematisches Institut Universität Würzburg D-97074 Würzburg, Germany
Studia Mathematica, Tome 198 (2010) no. 3, pp. 279-300 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study a class of operator polynomials in Hilbert space which are spectraloid in the sense that spectral radius and numerical radius coincide. The focus is on the spectrum in the boundary of the numerical range. As an application, the Eneström–Kakeya–Hurwitz theorem on zeros of real polynomials is generalized to Hilbert space.
DOI : 10.4064/sm198-3-7
Keywords: study class operator polynomials hilbert space which spectraloid sense spectral radius numerical radius coincide focus spectrum boundary numerical range application enestr kakeya hurwitz theorem zeros real polynomials generalized hilbert space

Jan Swoboda  1   ; Harald K. Wimmer  2

1 Max-Planck-Institut für Mathematik D-53111 Bonn, Germany
2 Mathematisches Institut Universität Würzburg D-97074 Würzburg, Germany 
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     title = {Spectraloid operator polynomials, the
 approximate numerical range and an
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     journal = {Studia Mathematica},
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Jan Swoboda; Harald K. Wimmer. Spectraloid operator polynomials, the
 approximate numerical range and an
 Eneström–Kakeya theorem in Hilbert space. Studia Mathematica, Tome 198 (2010) no. 3, pp. 279-300. doi: 10.4064/sm198-3-7

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