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Essential numerical range in $ B(l\sb{1})$

Authors: D. A. Legg and D. W. Townsend
Journal: Proc. Amer. Math. Soc. 81 (1981), 541-545
MSC: Primary 47A12
MathSciNet review: 601725
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Abstract: In recent years, the numerical range lifting problem has been solved for operators on $ {l_p}$, $ 1 < p < \infty $, and on certain Orlicz spaces $ {l_M}$. Specifically, given an operator $ A$, there exists a compact perturbation $ A + C$ such that the numerical range of $ A + C$ equals the essential numerical range of $ A$. This result has also been established for essentially Hermitian operators on $ {l_1}$. In the present paper, the authors establish this result for all operators on $ {l_1}$.

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Keywords: Essential numerical range, Calkin algebra, lifting problems, $ M$-ideal
Article copyright: © Copyright 1981 American Mathematical Society

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