Strongly strictly cyclic weighted shifts

Hedlund, James H.

doi:10.1090/S0002-9939-1976-0402530-1

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Strongly strictly cyclic weighted shifts
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by James H. Hedlund PDF

Proc. Amer. Math. Soc. 57 (1976), 119-121 Request permission

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

Domingo A. Herrero, Strictly cyclic weighted shifts, Rev. Un. Mat. Argentina 28 (1976/77), no. 2, 69–74. MR 467379
Edward Kerlin and Alan Lambert, Strictly cyclic shifts on $l_{p}$, Acta Sci. Math. (Szeged) 35 (1973), 87–94. MR 328658
Allen L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974, pp. 49–128. MR 0361899