It is an important result of Šemrl which states that every 2-local automorphism of the full operator algebra over a separable Hilbert space is necessarily an automorphism. In this paper we strengthen that result quite substantially for *-automorphisms. Indeed, we show that one can compress the defining two equations of 2-local *-automorphisms into one single equation, hence weakening the requirement significantly, but still keeping essentially the conclusion that such maps are necessarily *-automorphisms.
- 2-Local maps
- Algebra of Hilbert space operators
- Surjective isometries
ASJC Scopus subject areas
- Applied Mathematics