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

Tanaka, Ryotaro

doi:10.1090/proc/14536

Constructing a Lipschitz retraction from $\mathcal {B}(\mathcal {H})$ onto $\mathcal {K}(\mathcal {H})$
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Proc. Amer. Math. Soc. 147 (2019), 3919-3926 Request permission

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 $\mathcal {B}(\mathcal {H})$ of all bounded linear operators on a complex Hilbert space $\mathcal {H}$ onto the ideal $\mathcal {K}(\mathcal {H})$ consisting of all compact operators.

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