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Zeitschrift für Analysis und ihre Anwendungen

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Volume 1, Issue 2, 1982, pp. 7–9
DOI: 10.4171/ZAA/10

Published online: 1982-04-30

Theorems on polynomials in right invertible operators

Danuta Przeworska-Rolewicz[1]

(1) Polish Academy of Sciences, Warsaw 10, Poland

Suppose that $Q(D)$ is a polynomial in a right invertible operator acting in a linear space $X$, in general, with operator coefficients. Then $Q(D) = 0$ if and only if $Q(D) R^kz = 0$ for all $z \in \mathrm {ker} \: D (k = 0, 1, 2, \dots)$ under appropriate assumptions on $X$, the right inverse $R$ of $D$ and coefficients of $Q(D)$.

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Przeworska-Rolewicz Danuta: Theorems on polynomials in right invertible operators. Z. Anal. Anwend. 1 (1982), 7-9. doi: 10.4171/ZAA/10