11. A simple class of examples can be obtained by weakening the properties of unitary operators . 12. Note that the above decomposition of antiunitary operators contrasts with the spectral decomposition of unitary operators . 13. Unitary designs are especially useful in quantum computing since most operations are represented by unitary operators . 14. It thus defines a unitary operator . 15. Unitary operators are paramount to quantum theory, so unitary groups are important in particle physics.16. Thus a unitary operator is a bounded linear operator which is both an isometry and a coisometry. 17. The complexification is invariant under taking adjoints, since consists of unitary operators and of positive operators. 18. For example, by properties of the Borel functional calculus, we see that for any unitary operator , 19. Since " T " is a unitary operator , its spectrum lies on the unit circle. 20. For example, the Fourier inversion theorem on shows that the Fourier transform is a unitary operator on.
