ON THE UNIT SPHERE OF POSITIVE OPERATORS

Given a C*-algebra A, let S (A(+)) denote the set of positive elements in the unit sphere of A. Let H-1, H-2,H- H-3, and H-4 be complex Hilbert spaces, where H-3 and H-4 are infinite-dimensional and separable. In this article, we prove a variant of Tingley's problem by showing that every surjective isometry Delta : S(B(H-1)(+)) -> S(B(H-2)(+)) (resp., Delta : S (K(H-3)(+)) -> S(K(H-4)(+)))admits a unique extension to a surjective complex linear isometry from B(H-1 onto B(H-2) (resp., from K (H-3) onto K (H-4)). This provides a positive answer to a conjecture recently posed by Nagy.