Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A12

Retrieve articles in all journals with MSC: 47A12

Additional Information

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