An invariant of a pair of almost commuting unbounded operators

DOI10.1007/BF02463216zbMATH Open0958.47012arXivfunct-an/9702013MaRDI QIDQ1966245

Vladimir M. Manuilov

Publication date: 4 April 2001

Published in: Functional Analysis and Its Applications (Search for Journal in Brave)

Abstract: For a wide class of pairs of unbounded selfadjoint operators with bounded commutator we construct a K-theoretical integer invariant which is continuous, is equal to zero for commuting operators and is equal to one for the pair (x, i d/dx).

Full work available at URL: https://arxiv.org/abs/funct-an/9702013

zbMATH Keywords

perturbationssymmetric operatorcommutatorhomotopy invariant\(K\)-theoretic integer-valued invariant

Mathematics Subject Classification ID

Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Spectrum, resolvent (47A10) Perturbation theory of linear operators (47A55) Linear symmetric and selfadjoint operators (unbounded) (47B25) Commutators, derivations, elementary operators, etc. (47B47) Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) (47L80)

Cites Work

• Invariants of almost commuting unitaries
• Title not available (Why is that?)
• Title not available (Why is that?)

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