Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Uniform operators

Authors: Hsiao Lan Wang and Joseph G. Stampfli
Journal: Trans. Amer. Math. Soc. 289 (1985), 163-169
MSC: Primary 47A15; Secondary 47A65, 47B35
MathSciNet review: 779057
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A general representation theorem for uniform operators is obtained which enables one to verify a conjecture of Cowen and Douglas in the presence of a mild additional restriction.

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

  • [1] Arne Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 17. MR 0027954
  • [2] M. J. Cowen and R. G. Douglas, On moduli for invariant subspaces, Invariant subspaces and other topics (Timişoara/Herculane, 1981), Operator Theory: Adv. Appl., vol. 6, Birkhäuser, Basel-Boston, Mass., 1982, pp. 65–73. MR 685454
  • [3] W. F. Donoghue Jr., The lattice of invariant subspaces of a completely continuous quasi-nilpotent transformation, Pacific J. Math. 7 (1957), 1031–1035. MR 0092124
  • [4] R. G. Douglas, Structure theory for operators. I, J. Reine Angew. Math. 232 (1968), 180–193. MR 0238114
  • [5] N. K. Nikol′skiĭ, Unicellularity and non-unicellularity of weighted shift operators, Dokl. Akad. Nauk SSSR 172 (1967), 287–290 (Russian). MR 0217639
  • [6] D. Sarason, Invariant subspaces and unstarred operator algebras, Pacific J. Math. 17 (1966), 511–517. MR 0192365
  • [7] Donald Sarason, Weak-star density of polynomials, J. Reine Angew. Math. 252 (1972), 1–15. MR 0295088
  • [8] H. Wang, On uniform operators, Thesis, Indiana Univ., 1982.
  • [9] Herman Wold, A study in the analysis of stationary time series, Almqvist and Wiksell, Stockholm, 1954. 2d ed; With an appendix by Peter Whittle. MR 0061344

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47A15, 47A65, 47B35

Retrieve articles in all journals with MSC: 47A15, 47A65, 47B35

Additional Information

Keywords: Uniform operator, cyclic vector, invariant subspace, Toeplitz operator
Article copyright: © Copyright 1985 American Mathematical Society