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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A unicellular universal quasinilpotent weighted shift


Author: Domingo A. Herrero
Journal: Proc. Amer. Math. Soc. 110 (1990), 649-652
MSC: Primary 47B37; Secondary 47A55, 47A99
MathSciNet review: 1023343
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1023343-3
PII: S 0002-9939(1990)1023343-3
Keywords: Universal quasinilpotent, unilateral weighted shift, strictly cyclic operator, unicellular operator
Article copyright: © Copyright 1990 American Mathematical Society