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# A Unicellular Universal Quasinilpotent Weighted Shift

Domingo A. Herrero
Proceedings of the American Mathematical Society
Vol. 110, No. 3 (Nov., 1990), pp. 649-652
DOI: 10.2307/2047905
Stable URL: http://www.jstor.org/stable/2047905
Page Count: 4
For a suitably chosen sequence of weights $\{\alpha_n \}$, the unilateral weighted shift Q on $l^p (1 \leq p < \infty)$, defined by Qen = αne n + 1 (n ≥ 1), is a unicellular quasinilpotent operator such that Qk is not compact for any power k ≥ 1. As a corollary, several applications to approximation of Hilbert space operators are given.