## Abstract

A scalar function f is called opertor differentiable if its extension via spectral theory to the self-adjoint members of {Mathematical expression}(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 {Mathematical expression} We give a new condition under which this mapping is bounded on {Mathematical expression}(H). We also present a means of extending f to a function on all of {Mathematical expression}(H) and determine corresponding perturbation and differentiation formulas. A connection with the "joint Peirce decomposition" from the theory of JB^{*}-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 a C^{*}-algebra.

Original language | English |
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Pages (from-to) | 461-487 |

Number of pages | 27 |

Journal | Integral Equations and Operator Theory |

Volume | 13 |

Issue number | 4 |

DOIs | |

State | Published - Jul 1990 |

## ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory