REMARKS ON COMPLEMENTED SUBSPACES OF VONNEUMANN-ALGEBRAS Academic Article uri icon

abstract

  • SynopsisIn this note we include two remarks about bounded (not necessarily contractive) linear projections on a von Neumann algebra. We show that if M is a von Neumann subalgebra of B(H) which is complemented in B(H) and isomorphic to MM, then M is injective (or equivalently M is contractively complemented). We do not know how to get rid of the second assumption on M. In the second part, we show that any complemented reflexive subspace of a C*-algebra is necessarily linearly isomorphic to a Hilbert space.

published proceedings

  • PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS

author list (cited authors)

  • PISIER, G.

citation count

  • 9

complete list of authors

  • PISIER, G

publication date

  • January 1992