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LEFT SYMMETRIC POINTS FOR BIRKHOFF ORTHOGONALITY IN THE PREDUALS OF VON NEUMANN ALGEBRAS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 98 / Issue 3 / December 2018
- Published online by Cambridge University Press:
- 28 August 2018, pp. 494-501
- Print publication:
- December 2018
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- Article
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In this paper, we give a complete description of left symmetric points for Birkhoff orthogonality in the preduals of von Neumann algebras. As a consequence, except for
$\mathbb{C}$, 
$\ell _{\infty }^{2}$ and 
$M_{2}(\mathbb{C})$, there are no von Neumann algebras whose preduals have
nonzero left symmetric points for Birkhoff orthogonality.
