Constructing a Lipschitz retraction from ℬ(ℋ) onto 𝒦(ℋ)

Abstract

It is shown that each norm closed proper two-sided ideal of a von Neumann algebra is a Lipschitz retract of the algebra. In particular, there exists a Lipschitz retraction from the algebra B ( H ) \mathcal {B}(\mathcal {H}) of all bounded linear operators on a complex Hilbert space H \mathcal {H} onto the ideal K ( H ) \mathcal {K}(\mathcal {H}) consisting of all compact operators.