Weak commutation relations of unbounded operators andapplications

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Abstract

Four possible definitions of the commutation relation [S, T] = 11 of two closableunbounded operators S, T are compared. The weak sense of this commutator isgiven in terms of the inner product of the Hilbert space H where the operators act.Some consequences on the existence of eigenvectors of two numberlike operators arederived and the partial O*-algebra generated by S, T is studied. Some applicationsare also considered.
Original languageEnglish
Number of pages14
JournalJournal of Mathematical Physics
Volume52
Publication statusPublished - 2011

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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