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Kaplansky's Quasitrace Conjecture

Kaplansky's quasitrace conjecture asserts that every normalized 2-quasitrace on a unital complex C*-algebra is a tracial state. The extension to M_2(A) is part of the hypothesis; a quasitrace without that extension does not answer this question.

A unital C*-algebra is properly infinite when it contains two isometries with orthogonal ranges.

See also

Group C*-Algebra, Quasitrace, Stably Finite C*-Algebra, Tracial State

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References

Blackadar, B. Operator Algebras: Theory of C*-Algebras and von Neumann Algebras. Berlin, Germany: Springer, 2006. https://doi.org/10.1007/3-540-28517-2.Schafhauser, C.; Tikuisis, A.; and White, S. "Nuclear C^*-Algebras: 99 Problems." 12 Jun 2025. https://arxiv.org/abs/2506.10902.

Cite this as:

Weisstein, Eric W. "Kaplansky's Quasitrace Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/KaplanskysQuasitraceConjecture.html

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