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The Howland-Kato Commutator Problem II

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arxiv 1909.06514 v1 pith:NIMZPP2H submitted 2019-09-14 math.FA math-phmath.MP

Ira Herbst This is my paper · ORCID
classification math.FAmath-phmath.MP
keywords commutatoroperatorproblemboundedconcentratecontinuediscussfinite
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We continue to discuss the following problem: For which bounded measurable real functions f and g is the commutator i[f(P),g(Q)] a non-negative operator on L^2(R)? In this work we concentrate on the situation where the commutator is a finite rank operator.

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  1. A counterexample to the Kato conjecture for positive commutators

    math.FA 2026-08 conditional novelty 8.0 of 10

    The commutator i[arctan(P), arctan(Q)] is nonnegative with trace pi/2, disproving the Kato conjecture.

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