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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.

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