New York Journal of Mathematics
Volume 27 (2021), 1085-1095


Isaac Goldbring

Oracle computability of conditional expectations onto subfactors

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Published: July 24, 2021.
Keywords: conditional expectations, tracial von Neumann algebras, existentially closed structures, oracle computability.
Subject: 03C57, 03C66, 46L37, 22D55.

We initiate the effective study of conditional expectations onto subfactors. Our main result is that if M is an existentially closed II1 factor with a w-spectral gap subfactor N, then the conditional expectation function onto N can be computed from a (Turing) oracle that computes a presentation of M, the inclusion of N into M, and a spectral gap function for the pair (M,N).


I. Goldbring was partially supported by NSF CAREER grant DMS-1349399.

Author information

Isaac Goldbring:
Department of Mathematics
University of California at Irvine
340 Rowland Hall (Bldg. # 400)
Irvine, CA 92697-3875, USA