Splittings of Banach spaces induced by Clifford algebras
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- by N. L. Carothers, S. J. Dilworth and David Sobecki PDF
- Proc. Amer. Math. Soc. 128 (2000), 1347-1356 Request permission
Abstract:
Let $H$ be an infinite-dimensional Hilbert space of density character $\mathfrak {m}$. By representing $H$ as a module over an appropriate Clifford algebra, it is proved that $H$ possesses a family $\{A_{\alpha }\}_{\alpha \in \mathfrak {m}}$ of proper closed nonzero subspaces such that \begin{equation*}d(S_{A_{\alpha }},S_{A_{\beta }})=d(S_{A^{\perp }_{\alpha }},S_{A_{\beta }}) =d(S_{A^{\perp }_{\alpha }},S_{A^{\perp }_{\beta }})=\sqrt {2-\sqrt 2}\qquad (\alpha \ne \beta ).\end{equation*} Analogous results are proved for $L_{p}$ spaces and for $c_{0}(X)$ and $\ell _{p}(X)$ ($1 \le p \le \infty$) when $X$ is an arbitrary nonzero Banach space.References
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Additional Information
- N. L. Carothers
- Affiliation: Department of Mathematics, Bowling Green State University, Bowling Green, Ohio 43402
- Email: carother@math.bgsu.edu
- S. J. Dilworth
- Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
- MR Author ID: 58105
- Email: dilworth@math.sc.edu
- David Sobecki
- Affiliation: Department of Mathematics, Miami University, Hamilton, Ohio 45014
- Email: sobeckdm@muohio.edu
- Received by editor(s): June 19, 1998
- Published electronically: October 18, 1999
- Communicated by: Dale Alspach
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1347-1356
- MSC (1991): Primary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-99-05374-5
- MathSciNet review: 1670426