Constructing a Lipschitz retraction from $\mathcal {B}(\mathcal {H})$ onto $\mathcal {K}(\mathcal {H})$
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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.References
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Additional Information
- Ryotaro Tanaka
- Affiliation: Faculty of Industrial Science and Technology, Tokyo University of Science, Oshamanbe, Hokkaido 049-3514, Japan
- MR Author ID: 1007696
- ORCID: 0000-0003-2482-9203
- Email: r-tanaka@rs.tus.ac.jp
- Received by editor(s): November 21, 2018
- Received by editor(s) in revised form: January 5, 2019, and January 8, 2019
- Published electronically: April 18, 2019
- Communicated by: Stephen Dilworth
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3919-3926
- MSC (2010): Primary 46B80; Secondary 46B20, 47L99
- DOI: https://doi.org/10.1090/proc/14536
- MathSciNet review: 3993784