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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.
Jan Swoboda, and Harald K. Wimmer. "Spectraloid operator polynomials, the approximate numerical range and an Eneström-Kakeya theorem in Hilbert space." Studia Mathematica 198.3 (2010): 279-300. <http://eudml.org/doc/285890>.
@article{JanSwoboda2010, abstract = {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.}, author = {Jan Swoboda, Harald K. Wimmer}, journal = {Studia Mathematica}, language = {eng}, number = {3}, pages = {279-300}, title = {Spectraloid operator polynomials, the approximate numerical range and an Eneström-Kakeya theorem in Hilbert space}, url = {http://eudml.org/doc/285890}, volume = {198}, year = {2010}, }
TY - JOUR AU - Jan Swoboda AU - Harald K. Wimmer TI - Spectraloid operator polynomials, the approximate numerical range and an Eneström-Kakeya theorem in Hilbert space JO - Studia Mathematica PY - 2010 VL - 198 IS - 3 SP - 279 EP - 300 AB - 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. LA - eng UR - http://eudml.org/doc/285890 ER -