Fubini theorem in noncommutative geometry
Fedor Sukochev, Dmitriy Zanin
TL;DR
This paper investigates the Fubini theorem within noncommutative geometry, establishing conditions under which it holds, and providing examples where it does not, thus clarifying its applicability in this mathematical framework.
Contribution
It introduces a natural sufficient condition related to heat semigroup asymptotics for the Fubini formula to hold in spectral triples, and presents counterexamples.
Findings
Fubini formula holds under specific spectral triple conditions
Counterexamples demonstrate failure of Fubini in some cases
Heat semigroup asymptotics are key to the formula's validity
Abstract
We discuss the Fubini formula in Alain Connes' noncommutative geometry. We present a sufficient condition on spectral triples for which a Fubini formula holds true. The condition is natural and related to heat semigroup asymptotics. We provide examples of spectral triples for which the Fubini formula fails.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Algebraic structures and combinatorial models