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

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] A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1949), 239-255. MR 0027954 (10:381e)
  • [2] M. J. Cowen and R. G. Douglas, On moduli for invariant subspaces, Invariant Subspaces and Other Topics (Timisoara/Herculane, 1981), Operator Theory: Advanced Applications, 6, Birkhauser, Basel, 1882, pp. 65-73. MR 685454 (84b:47007)
  • [3] W. F. Donahue, The lattice of invariant subspaces of a completely continuous quasi-nilpotent transformation, Pacific J. Math. 7 (1957), 1031-1035. MR 0092124 (19:1066f)
  • [4] R. G. Douglas, Structure theory of operators. I, J. Reine Angew. Math. 232 (1968), 180-193. MR 0238114 (38:6390)
  • [5] N. K. Nikol'skii, The unicellularity and nonunicellularity of weighted shift operators, Dokl. Akad. Nauk SSSR 172 (1967), no. 2; English transl., Soviet Math. Dokl. 8 (1967), 91-94. MR 0217639 (36:728)
  • [6] D. Sarason, Invariant subspaces and unstarred algebra, Pacific J. Math. 17 (1966), 511-518. MR 0192365 (33:590)
  • [7] -, Weak-star density of polynomials, J. Reine Angew. Math. 252 (1972), 1-15. MR 0295088 (45:4156)
  • [8] H. Wang, On uniform operators, Thesis, Indiana Univ., 1982.
  • [9] H. Wold, A study in the analysis of stationary time series, Almqvist & Wiksell, Stockholm, 1938. MR 0061344 (15:811d)

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

American Mathematical Society