One-sided projections on C*-algebras Academic Article uri icon

abstract

  • We obtain several equivalent characterizations of linear maps on a C*-algebra A which are given by left multiplication by a fixed orthogonal projection in (resp. fixed element in) A or its multiplier algebra. These results are connected to the 'complete one-sided M-ideals' in operator spaces recently introduced by Blecher, Effros, and Zarikian. Part of the proof makes use of a technique to "solve" multi-linear equations in von Neumann algebras. This technique is also applied to show that preduals of von Neumann algebras have no nontrivial complete one-sided M-ideals. We also show that the intersection of two complete one-sided M-summands need not be a one-sided M-summand.

author list (cited authors)

  • Blecher, D. P., Smith, R. R., & Zarikian, V.

complete list of authors

  • Blecher, DP||Smith, RR||Zarikian, V

publication date

  • December 2004