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Journal of Operator Theory

Volume 36, Issue 1, Summer 1996  pp. 45-58.

Linear mappings that preserve operators annihilated by a polynomial

Authors Peter Semrl
Author institution: Faculty of Mechanical Engineering, University of Maribor, Smetanova, 17, 62000 Maribor, Slovenia

Summary:  Let H be an infinite-dimensional Hilbert space, and let f(x) be a complex polynomial with $deg(f) \ge 2$. We find the general form of surjective linear mappings $\varphi : \mathcal B(H) \to \mathcal B(H)$ that preserve operator roots of f(X) = 0 in both directions.

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