Characterizing projections among positive operators in the unit sphere Peralta Pereira, Antonio Miguel Let E and P be subsets of a Banach space X, and let us define the unit sphere around E in P as the set Sph(E; P) := {x is an element of P : parallel to x - b parallel to = 1 for all b is an element of E}. Given a C*-algebra A and a subset E subset of A; we shall write Sph(+) (E) or Sph(A)(+) (E) for the set Sph(E; S(A(+))); where S(A(+)) denotes the unit sphere of A(+). We prove that, for every complex Hilbert space H, the following statements are equivalent for every positive element a in the unit sphere of B(H): (a) a is a projection; (b) Sph(B)((H))(+) (Sph(B)((H))(+) ({a})) = {a}. We also prove that the equivalence remains true when B(H) is replaced with an atomic von Neumann algebra or with K(H-2), where H-2 is an infinite-dimensional and separable complex Hilbert space. 2019-11-27T12:27:27Z 2019-11-27T12:27:27Z 2018-04 journal article Peralta, A. M. (2018). Characterizing projections among positive operators in the unit sphere. Advances in Operator Theory, 3(3), 731-744. http://hdl.handle.net/10481/58094 10.15352/aot.1804-1343 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ open access Atribución-NoComercial-SinDerivadas 3.0 España Springer Nature