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Strongly strictly cyclic weighted shifts


Author: James H. Hedlund
Journal: Proc. Amer. Math. Soc. 57 (1976), 119-121
MSC: Primary 47B37
DOI: https://doi.org/10.1090/S0002-9939-1976-0402530-1
MathSciNet review: 0402530
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Abstract: An example is given of a unilateral weighted shift on complex Hilbert space which is strictly cyclic but not strongly strictly cyclic. Similar examples of weighted shifts on the sequence spaces $ {l^p}$, for $ 1 < p < \infty $, are indicated.


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

  • [1] D. A. Herrero, Strictly cyclic weighted shifts (preprint). MR 0467379 (57:7238)
  • [2] E. Kerlin and A. L. Lambert, Strictly cyclic shifts on $ {l_p}$, Acta Sci. Math. (Szeged) 35 (1973), 87-94. MR 48 #7000. MR 0328658 (48:7000)
  • [3] A. L. Shields, Weighted shift operators and analytic function theory, Math. Surveys, vol. 13, Amer. Math. Soc., Providence, R.I., 1974, pp. 49-128. MR 0361899 (50:14341)

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DOI: https://doi.org/10.1090/S0002-9939-1976-0402530-1
Article copyright: © Copyright 1976 American Mathematical Society

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