A "typical" contraction is unitary

Details A "typical" contraction is unitary A "typical" contraction is unitary

2008-07-12

arxiv.org/abs/0807.1994v1

Mathematics

Functional Analysis

5 pages

Scientific paper

We show that (for the weak operator topology) the set of unitary operators on
a separable infinite-dimensional Hilbert space is residual in the set of all
contractions. The analogous result holds for isometries and the strong operator
topology as well. These results are applied to the problem of embedding
operators into strongly continuous semigroups.

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