2-Local Isometries of Some Operator Algebras

As a consequence of the main result of the paper we obtain that every 2-local isometry of the C^*-algebra $B(H)$ of all bounded linear operators on a separable infinite-dimensional Hilbert space H is an isometry. We have a similar statement concerning the isometries of any extension of the algebra of all compact operators by a separable commutative C^*-algebra. Therefore, on those C^*-algebras the isometries are completely determined by their local actions on the two-point subsets of the underlying algebras. AMS 2000 Mathematics subject classification: Primary 47B49