On the Quasitrace Problem and a Characterization of W*-algebras

Alec Gow

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arXiv · 2601.04431

On the Quasitrace Problem and a Characterization of W*-algebras

Alec Gow

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Abstract

We conjecture that a unital C*-algebra is a W*-algebra if and only if each of its maximal abelian self-adjoint subalgebras is a W*-algebra; this is a space-free analogue of a known result due to G.K. Pedersen. Our main result is a proof that this conjecture holds for finite C*-algebras if and only if every $2$-quasitrace on a unital C*-algebra is a trace. We also show that the spatial condition in Pedersen's Theorem can be substantially weakened for AW*-factors. Finally, we give a new characterization of Type II$_1$ W*-factors among Type II$_1$ AW*-factors, which allows us to relate the question of (quasi)linearity of functionals on finite AW*-algebras to the question of monotone completeness of AW*-algebras.

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BibTeX RIS

Alec Gow. 2026-01-07. On the Quasitrace Problem and a Characterization of W*-algebras. https://arxiv.org/abs/2601.04431

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