A unicellular universal quasinilpotent weighted shift

Herrero, Domingo A.

doi:10.1090/S0002-9939-1990-1023343-3

A unicellular universal quasinilpotent weighted shift
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Proc. Amer. Math. Soc. 110 (1990), 649-652 Request permission

Abstract:

For a suitably chosen sequence of weights $\{ {\alpha _n}\}$, the unilateral weighted shift $Q$ on ${l^p}(1 \leq p < \infty )$, defined by $Q{e_n} = {\alpha _n}{e_{n + 1}}(n \geq 1)$, is a unicellular quasinilpotent operator such that ${Q^k}$ is not compact for any power $k \geq 1$. As a corollary, several applications to approximation of Hilbert space operators are given.

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