Say that an automorphism of a unital C*-algebra is locally inner if on any element it agrees with some inner automorphism. We discuss whether, for various classes of C*-algebras and von Neumann algebras, a locally inner automorphism must be inner. We also employ this concept to answer the question: does the diagonal sum descend to a well-defined map on the automorphism orbits of a unital C*-algebra? (By the "diagonal sum" of two elements we simply mean the 2x2 matrix which has the given elements on the diagonal.)
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Last updated 15 April 2008. This page was created and is maintained by Stephen Wills (s.wills@ucc.ie).