Numerical ranges of conjugations and antilinear operators on a Banach space

Muneo Cho, Injo Hur, Ji Eun Lee


In this paper, we prove that the numerical range of a conjugation on Banach spaces, using the connected property, is either the unit circle or the unit disc depending the dimension of the given Banach space. When a Banach space is reflexive,  we have the same result for the numerical range of a conjugation by applying path-connectedness which is applicable to the Hilbert space setting. In addition, we show that the numerical ranges of antilinear operators on Banach spaces are contained in annuli.


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