A ``typical'' contraction is unitary (Q536450)

The author proves that the set \(\mathcal U\) of the unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all the contractions with the weak operator topology. Furthermore, \(\mathcal U\) is also residual in the set of the isometries relative to the strong operator topology. In addition, the previous results are applied to the embedding problem of bounded linear operators into strongly continuous semigroups. Also, the continuous analogue of the main theorem is studied.