Resumen de Maps preserving fixed points of generalized product of operators

Youssef Bouramdane, Mustapha Ech-Cherif El Kettani, A. Elhiri, A. Lahssaini

• Let B(X) be the algebra of all bounded linear operators in a complex Banach space X. For A ? B(X) let F (A) be the subspace of fixed point of A. For an integer k ? 2, let (i1, .., im) be a finite sequence with terms chosen from {1, · · · , k}, and assume at least one of the terms in (i1, · · · , im) appears exactly once. The generalized product of k operators A1, ..., Ak ? B(X) is defined by A1 ? A2 ? · · · ? Ak = Ai? Ai? · · · Aim , and includes the usual product and the triple product. We characterize the form of maps from B(X) onto itself satisfying F (?(A1) ? · · · ? ?(Ak)) = F (A1 ? · · · ? Ak) for all A1, · · · , Ak ? B(X).