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Sobre la ecuación cuadrática en operadores A + BT +TC + TDT = 0.

Vicente Hernández, Lucas Jódar (1983)

Stochastica

By means of the application of annihilating entire functions of an operator, the bilateral quadratic equation in operators A + BT +TC + TDT = 0, is changed into an unilateral linear equation, obtaining conditions under which the solutions of such linear equation satisfy the quadratic equation.

Spectral factorization of measurable rectangular matrix functions and the vector-valued Riemann problem.

Marek Rakowski, Ilya Spitkovsky (1996)

Revista Matemática Iberoamericana

We define spectral factorization in Lp (or a generalized Wiener-Hopf factorization) of a measurable singular matrix function on a simple closed rectifiable contour Γ. Such factorization has the same uniqueness properties as in the nonsingular case. We discuss basic properties of the vector valued Riemann problem whose coefficient takes singular values almost everywhere on Γ. In particular, we introduce defect numbers for this problem which agree with the usual defect numbers in the case of a nonsingular...

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

Jan Swoboda, Harald K. Wimmer (2010)

Studia Mathematica

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.

Stability of infinite ranges and kernels

K.-H. Förster, V. Müller (2006)

Studia Mathematica

Let A(·) be a regular function defined on a connected metric space G whose values are mutually commuting essentially Kato operators in a Banach space. Then the spaces R ( A ( z ) ) and N ( A ( z ) ) ¯ do not depend on z ∈ G. This generalizes results of B. Aupetit and J. Zemánek.

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