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Characterizing projections among positive operators in the unit sphere
dc.contributor.author | Peralta Pereira, Antonio Miguel | |
dc.date.accessioned | 2019-11-27T12:27:27Z | |
dc.date.available | 2019-11-27T12:27:27Z | |
dc.date.issued | 2018-04 | |
dc.identifier.citation | Peralta, A. M. (2018). Characterizing projections among positive operators in the unit sphere. Advances in Operator Theory, 3(3), 731-744. | es_ES |
dc.identifier.uri | http://hdl.handle.net/10481/58094 | |
dc.description.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. | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | Springer Nature | es_ES |
dc.rights | Atribución-NoComercial-SinDerivadas 3.0 España | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.title | Characterizing projections among positive operators in the unit sphere | es_ES |
dc.type | journal article | es_ES |
dc.rights.accessRights | open access | es_ES |
dc.identifier.doi | 10.15352/aot.1804-1343 |