Monotone Unitary Families
نویسنده
چکیده
A unitary family is a family of unitary operators U(x) acting on a finite dimensional hermitian vector space, depending analytically on a real parameter x. It is monotone if 1 i U (x)U(x) is a positive operator for each x. We prove a number of results generalizing standard theorems on the spectral theory of a single unitary operator U0, which correspond to the ’commutative’ case U(x) = eU0. Also, for a two-parameter unitary family – for which there is no analytic perturbation theory – we prove an implicit function type theorem for the spectral data under the assumption that the family is monotone in one argument.
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