Abstract
A scalar functionf is called opertor differentiable if its extension via spectral theory to the self-adjoint members of\(\mathfrak{B}\)(H) is differentiable. The study of differentiation and perturbation of such operator functions leads to the theory of mappings defined by the double operator integral
We give a new condition under which this mapping is bounded on\(\mathfrak{B}\)(H). We also present a means of extendingf to a function on all of\(\mathfrak{B}\)(H) and determine corresponding perturbation and differentiation formulas. A connection with the “joint Peirce decomposition” from the theory ofJB *-triples is found. As an application we broaden the class of functions known to preserve the domain of the generator of a strongly continuous one-parameter group of*-automorphisms of aC *-algebra.
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Partially supported by NSF grant DMS8603064.
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Arazy, J., Barton, T.J. & Friedman, Y. Operator differentiable functions. Integr equ oper theory 13, 461–487 (1990). https://doi.org/10.1007/BF01210398
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DOI: https://doi.org/10.1007/BF01210398