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Journal of Operator Theory

Volume 86, Issue 1, Summer 2021  pp. 17-29.

Maximal amenability with asymptotic orthogonality in amalgamated free products

Authors:  Brian Leary
Author institution: Department of Mathematics, West Virginia University Institute of Technology, Beckley, WV, 25801, U.S.A.

Summary: We investigate the use of Popa's asymptotic orthogonality to establish maximal amenability for amalgamated free product von Neumann algebras. Although new techniques have recently been developed to consider amalgamated free products, we find that the technique developed by Popa in the 1980s can be used to demonstrate maximal amenability for a certain family of amalgamated free product von Neumann algebras.

Keywords: amalgamated free product von Neumann algebras, asymptotic orthogonality, maximal amenable subalgebras, Pimsner--Popa basis, Popa's intertwining-by-bimodules.

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