An Elementary Approach to Operator Lipschitz Type Estimates
The paper brings an elementary approach to Lipschitz type estimates for functions of operators. The approach is based on the reduction to the case of operators on finite-dimensional inner product spaces. This allows us to avoid double and triple operator integrals and consider instead double and triple operator sums. Unlike in the case of double and triple operator integrals, double and triple operator sums can be defined for arbitrary functions which completely eliminates the problem of definitions of double operator integrals and various types of triple operator integrals.
KeywordsFunctions of commuting operators functions of noncommuting operators Lipschitz type estimates functions of perturbed operators double operator sums triple operator sums Besov spaces
Mathematics Subject Classification (2010)Primary 47A55 Secondary 47A60 47A63 47B10 46E39
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