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A note on strictly cyclic weighted shifts

A note on strictly cyclic weighted shifts

We answer negatively Shields' Question 15 in [1].The object of this note is to answer negatively one of the many questions raised by Allen L. Shields in his article [1].Question 15 of [1] is: If T is a unilateral weighted shift with weights wn decreasing to 1 and if 2"_0yS(n)~2 …