On normal approximate spectrum

Mathematical Subject Classifications (2000): 47A10, 47A56, 47A12Keywords: Operator polynomials, Eneström-Kakeya theorem, normal approximate eigenvalues, semisimple eigenvalues, Jordan chains, approximate point spectrum, residual spectrum, spectral radius, numerical range, numerical radius, spectraloid operator. Running title: Operator polynomialsAbstract: In this paper 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.

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“…[16], [19], [30]). The case where (λI − T )v= 0 is equivalent to (λI − T ) * v= 0 is of special interest.…”

Section: ) If and Only Ifmentioning

confidence: 99%

Spectraloid operator polynomials, the approximate numerical range and an Eneström–Kakeya theorem in Hilbert space

Swoboda

Wimmer

2010

Studia Math.

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“…The remainder of the proof runs along the line of the proof of [6; Theorem 1]. 4. oint approximate spectrum.…”

Section: Fujhmentioning

confidence: 99%

“…V 417 linear functional of . We shall show the following reciprocity theorem proved in [4] and [9]" Theorem 1.…”

mentioning

confidence: 93%

“…approximate propervalues of an operator T and the characters of the unital C*-algebra generated by T. He established, among others, the reciprocity for hyponormal operators. The reciprocity for general operators is obtained in [4] and [9]. In the present note, we shall give an alternative proof of the reciprocity basing on the Berberian representation of an operator established by Berberian [1]" Theorem A (Berberian).…”

mentioning

confidence: 98%

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