7 papers
A Note on Pseudofinite W*-Probability Spaces
Jananan Arulseelan
We introduce pseudofinite W*-probability spaces. These are W*-probability spaces that are elementarily equivalent to Ocneanu ultraproducts of finite-dimensional von Neumann algebra…
Pointwise Mean Value Theorems in Constructive Mathematics
Jananan Arulseelan, James E. Hanson
We answer some questions regarding the mean value theorem and related results in constructive mathematics. The answers to these questions reveal interesting properties of the Mean…
The Universal Theory of Locally Universal Tracial von Neumann Algebras is not Computable
Jananan Arulseelan, Aareyan Manzoor
Building on Lin's breakthrough MIP = coRE and an encoding of non-local games as universal sentences in the language of tracial von Neumann algebras, we show that locally uni…
Model Theory of General von Neumann Algebras II: Group Actions and Crossed Products
Jananan Arulseelan
Expanding on previous work of the author, we initiate the model theoretic study of W-dynamical systems. We axiomatize continuous weight-preserving group actions of on von N…
Model Theory of General von Neumann Algebras I: Generalized Ocneanu Ultraproducts
Jananan Arulseelan
This paper collates, presents, and expands upon technology and results obtained as part of the author's PhD thesis. We generalize work done in the -finite setting by the author…
Totally Bounded Elements in W*-probability Spaces
Jananan Arulseelan, Isaac Goldbring, Bradd Hart +1
We introduce the notion of a totally (-) bounded element of a W*-probability space and, borrowing ideas of Kadison, give an intrinsic characterization of the -suba…