ABSTRACT
Theorem 13.4.1(2) on the eigenvectors and the spectral decomposition of unitary operators on V → N https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203702413/2f242b9b-104e-4a03-b478-d3f6577cf44e/content/eq4601.tif"/> needs to be modified to apply to an infinite-dimensional Hilbert space H → https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203702413/2f242b9b-104e-4a03-b478-d3f6577cf44e/content/eq4602.tif"/> . This is because unitary operators on H → https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203702413/2f242b9b-104e-4a03-b478-d3f6577cf44e/content/eq4603.tif"/> may have a continuous spectrum. This is similar to the corresponding situation for selfadjoint operators. As with selfadjoint operators the problem is solved by the introduction of spectral functions for unitary operators.
