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Transactions of the American Mathematical Society

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The absolute continuity of phase operators

Authors: J. Dombrowski and G. H. Fricke
Journal: Trans. Amer. Math. Soc. 213 (1975), 363-372
MSC: Primary 47B15
MathSciNet review: 0377573
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Abstract: This paper studies the spectral properties of a class of operators known as phase operators which originated in the study of harmonic oscillator phase. Ifantis conjectured that such operators had no point spectrum. It was later shown that certain phase operators were, in fact, absolutely continuous and that all phase operators at least had an absolutely continuous part. The present work completes the discussion by showing that all phase operators are absolutely continuous.

References [Enhancements On Off] (What's this?)

  • [1] J. Dombrowski, Spectral properties of phase operators, J. Mathematical Phys. 15 (1974), 576-577. MR 0334757 (48:13075)
  • [2] P. R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, Chelsea, New York, 1951. MR 13, 563. MR 1653399 (99g:47001)
  • [3] E. K. Ifantis, Abstract formulation of the quantum mechanical oscillator phase problem, J. Mathematical Phys. 12 (1971), 1021-1026. MR 43 #5834. MR 0280113 (43:5834)
  • [4] E. C. Lerner, Harmonic-oscillator phase operators, Nuovo Cimento 56B (1968), 183-186.
  • [5] E. C. Lerner, H. W. Huang and G. E. Walters, Some mathematical properties of oscillator phase operators, J. Mathematical Phys. 11 (1970), 1679-1684. MR 41 #4973. MR 0260346 (41:4973)
  • [6] C. R. Putnam, Commutation properties of Hilbert space operators and related topics, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 36, Springer-Verlag, New York, 1967. MR 36 #707. MR 0217618 (36:707)

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Keywords: Phase operators, absolute continuity of phase operators, real parts of weighted shifts
Article copyright: © Copyright 1975 American Mathematical Society

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