Cyclic decomposition of unitary spaces (Q793977)

The main result of the present paper is: If \(\pi\) is a unitary transformation that is similar to its inverse, then the vector space V is an orthogonal sum of regular \(\pi\)-cyclic and \(\pi\)-bicyclic subspaces. For arbitrary unitary spaces this does not imply that \(\pi\) is a product of two unitary involutions, although \(\pi\) is a product of involutions in GL(V). But a unitary transformation \(\pi\) of a complex inner product space is a product of two unitary involutions if the spectrum of \(\pi\) is symmetric to the real axis.