Abstract
LetX be a complex Lebesgue space with a unique duality mapJ fromX toX *, the conjugate space ofX. LetA be a bounded linear operator onX. In this paper we obtain a non-linear eigenvalue problem for Λ(A)=sup{Reα: α ∈W(A} whereW(A)={J(x)A(x)) : ∥x∥=1}, under the assumption that Λ(A) and the convex hull ofW(A) for some linear operatorsA onl p , 2<p<∞.
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Fixman, U., Okoh, F. & Rao, G.K.R. An eigenvalue problem for the numerical range of a bounded linear operator. Integr equ oper theory 31, 421–435 (1998). https://doi.org/10.1007/BF01228100
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DOI: https://doi.org/10.1007/BF01228100