Abstract
It is proved that, for any Lipschitz function f(t1, ..., tn) of n variables, the corresponding map fop: (A1, ...,An) → f(A1, ..., An) on the set of all commutative n-tuples of Hermitian operators on a Hilbert space is Lipschitz with respect to the norm of each Schatten ideal Sp, p ∈ (1,∞). This result is applied to the functional calculus of normal operators and contractions. It is shown that Lipschitz functions of one variable preserve domains of closed derivations with values in Sp. It is also proved that the map fop is Frechet differentiable in the norm of Sp if f is continuously differentiable.
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