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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A commutativity theorem for semibounded operators in Hilbert space
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by A. Edward Nussbaum PDF
Proc. Amer. Math. Soc. 125 (1997), 3541-3545 Request permission

Abstract:

Let $A$ and $B$ be semibounded (bounded from below) operators in a Hilbert space $\mathfrak {H}$ and $\mathfrak {D}$ a dense linear manifold contained in the domains of $AB$, $BA$, $A^2$, and $B^2$, and such that $ABx=BAx$ for all $x$ in $\mathfrak {D}$. It is shown that if the restriction of $(A+B)^2$ to $\mathfrak {D}$ is essentially self-adjoint, then $A$ and $B$ are essentially self-adjoint and $\bar {A}$ and $\bar {B}$ commute, i.e. their spectral projections permute.
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Additional Information
  • A. Edward Nussbaum
  • Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130
  • Email: addi@math.wustl.edu
  • Received by editor(s): April 30, 1996

  • Dedicated: Dedicated to Allen Devinatz
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3541-3545
  • MSC (1991): Primary 47B25
  • DOI: https://doi.org/10.1090/S0002-9939-97-03977-4
  • MathSciNet review: 1402881