Abstract
In this paper it will be shown that the spectrum of every unicellular unilateral weighted shift operator on a symmetric Banach space is the singleton set {0}. From this, we give an affirmative answer to Rosenthal-Shields' problem.
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Project supported by the National Natural Science Foundation of China
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Fang, L. On Rosenthal-Shields' problem. Acta Mathematica Sinica 8, 189–203 (1992). https://doi.org/10.1007/BF02629939
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DOI: https://doi.org/10.1007/BF02629939