Abstract
We consider nonmonic quadratic polynomials acting on a general or on a finite-dimensional linear space as a continuation of our work in [7,8]. Conditions are given for the existence of right roots, if the coefficient operators have lower block triangular representations. In the finite-dimensional case we consider (in a certain sense, entrywise) nonnegative coefficient matrices in the general (reducible) case, and extend several earlier results from the case of irreducible coefficients. In particular, we generalize results of Gail, Hantler and Taylor [9]. We show that our general methods are sufficiently strong to prove a remarkable result by Butler, Johnson and Wolkowicz [3], proved there by ingenious ad hoc methods.
This work was completed with partial support of the Hungarian National Science Grant OTKA No T-047276 and partial support of the DAAD, the Technical University of Berlin and the Budapest University of Technology and Economics.
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Förster, K.H., Nagy, B. (2007). On Reducible Nonmonic Matrix Polynomials with General and Nonnegative Coefficients. In: Förster, KH., Jonas, P., Langer, H., Trunk, C. (eds) Operator Theory in Inner Product Spaces. Operator Theory: Advances and Applications, vol 175. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8270-4_6
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DOI: https://doi.org/10.1007/978-3-7643-8270-4_6
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