@misc{10481/58094,
year = {2018},
month = {4},
url = {http://hdl.handle.net/10481/58094},
abstract = {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.},
publisher = {Springer Nature},
title = {Characterizing projections among positive operators in the unit sphere},
doi = {10.15352/aot.1804-1343},
author = {Peralta Pereira, Antonio Miguel},
}