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Proceedings of the American Mathematical Society

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Continuity properties of the spectrum of operators on Lebesgue spaces


Author: Bruce A. Barnes
Journal: Proc. Amer. Math. Soc. 106 (1989), 415-421
MSC: Primary 47B38; Secondary 47A10
DOI: https://doi.org/10.1090/S0002-9939-1989-0969515-7
MathSciNet review: 969515
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Abstract: Fix $ 1 \leq p \leq s \leq \infty $. Let $ {T_x},x \in \left[ {p,s} \right]$, be the collection of bounded linear operators on the Lebesgue spaces $ {L^x}$ determined by some fixed operator $ T$. This paper concerns continuity properties of the map $ x \to \sigma \left( {{T_x}} \right)$.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0969515-7
Keywords: Linear operator, spectrum, spectral radius
Article copyright: © Copyright 1989 American Mathematical Society

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