Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

Cyclic operators, commutators, and absolutely continuous measures


Author: J. Dombrowski
Journal: Proc. Amer. Math. Soc. 100 (1987), 457-463
MSC: Primary 47B37
DOI: https://doi.org/10.1090/S0002-9939-1987-0891145-4
MathSciNet review: 891145
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Commutator equations are used to study the relationship between the tridiagonal matrix structure of an unbounded cyclic selfadjoint operator and its spectrum. Sufficient conditions are given for absolute continuity. Results are related to the study of systems of orthogonal polyomials for which the measure of orthogonality is supported on an unbounded subset of the real line.


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

  • [1] Joanne Dombrowski, Tridiagonal matrix representations of cyclic selfadjoint operators, Pacific J. Math. 114 (1984), no. 2, 325–334. MR 757504
  • [2] J. Dombrowski, Tridiagonal matrix representations of cyclic selfadjoint operators. II, Pacific J. Math. 120 (1985), no. 1, 47–53. MR 808928
  • [3] Attila Máté and Paul Nevai, Orthogonal polynomials and absolutely continuous measures, Approximation theory, IV (College Station, Tex., 1983) Academic Press, New York, 1983, pp. 611–617. MR 754400
  • [4] Paul G. Nevai, Orthogonal polynomials, Mem. Amer. Math. Soc. 18 (1979), no. 213, v+185. MR 519926, https://doi.org/10.1090/memo/0213
  • [5] C. R. Putnam, Commutation properties of Hilbert space operators and related topics, Ergebnisse der Math., No. 36, Springer, 1967.
  • [6] Marshall Harvey Stone, Linear transformations in Hilbert space, American Mathematical Society Colloquium Publications, vol. 15, American Mathematical Society, Providence, RI, 1990. Reprint of the 1932 original. MR 1451877

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B37

Retrieve articles in all journals with MSC: 47B37


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0891145-4
Keywords: Absolute continuity, commutators, orthogonal polynomials
Article copyright: © Copyright 1987 American Mathematical Society