Operator differentiable functions

J. Arazy, T. J. Barton, Y. Friedman

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)461-487
Number of pages27
JournalIntegral Equations and Operator Theory
Issue number4
StatePublished - Jul 1990

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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