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- W2913351344 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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper B left-parenthesis script upper H right-parenthesis> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>B</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>H</mml:mi> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {B}(mathcal {H})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of all bounded linear operators on a complex Hilbert space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper H> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>H</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {H}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> onto the ideal <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper K left-parenthesis script upper H right-parenthesis> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>K</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>H</mml:mi> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {K}(mathcal {H})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> consisting of all compact operators." @default.
- W2913351344 created "2019-02-21" @default.
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- W2913351344 date "2019-04-18" @default.
- W2913351344 modified "2023-09-27" @default.
- W2913351344 title "Constructing a Lipschitz retraction from ℬ(ℋ) onto 𝒦(ℋ)" @default.
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- W2913351344 doi "https://doi.org/10.1090/proc/14536" @default.
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