Cyclic decomposition of unitary spaces. (English) Zbl 0539.51008
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.
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