Journal of Operator Theory

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

Linear mappings that preserve operators annihilated by a polynomial

Authors: Peter Šemrl
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 $\rm deg(f) \ge 2$. 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.

Keywords: Linear preserver.

Contents Full-Text PDF