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Almost commuting self-adjoint operators and measurements
- Part of
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- Journal:
- Canadian Mathematical Communications / Volume 1 / 2026
- Published online by Cambridge University Press:
- 06 April 2026, e3
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- Article
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We study the problem when an n-tuple of self-adjoint operators in an infinite-dimensional separable Hilbert space H with small commutators is close to an n-tuple of commuting self-adjoint operators on
$H.$ We give an affirmative answer to the problem when the synthetic-spectrum and the essential synthetic-spectrum are close. Examples are also exhibited that, in general, the answer to the problem when 
$n\ge 3$ is negative even the associated Fredholm index vanishes. This is an attempt to solve a problem proposed by David Mumford related to quantum theory and measurements.
