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Operators commuting with a weighted shift. (English) Zbl 0189.13403


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[1] S. Banach, Theorie des operations lineaires, Hafner, New York, 1932.
[2] L. W. Cohen and Nelson Dunford, Transformations on sequence spaces, Duke Math. J. 3 (1937), no. 4, 689 – 701. · Zbl 0018.07101 · doi:10.1215/S0012-7094-37-00357-0
[3] Paul R. Halmos, Günter Lumer, and Juan J. Schäffer, Square roots of operators, Proc. Amer. Math. Soc. 4 (1953), 142 – 149. · Zbl 0050.34004
[4] Frigyes Riesz and Béla Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955. Translated by Leo F. Boron. · Zbl 0070.10902
[5] Juan J. Schäffer, More about invertible operators without roots, Proc. Amer. Math. Soc. 16 (1965), 213 – 219. · Zbl 0136.11803
[6] R. A. Gellar, Shift operators in Banach space, Dissertation, Columbia University, New York, N. Y., 1968.
[7] Ralph Gellar, Operators commuting with a weighted shift, Proc. Amer. Math. Soc. 23 (1969), 538 – 545. , https://doi.org/10.1090/S0002-9939-1969-0259641-X Ralph Gellar, Cyclic vectors and parts of the spectrum of a weighted shift, Trans. Amer. Math. Soc. 146 (1969), 69 – 85.
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