Geodesic
Numerical ranges of conjugations and antilinear operators on a Banach space
Filomat, Tome 35 (2021) no. 8, p. 2715

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DOI

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
DOI : 10.2298/FIL2108715C
Classification : 47A12, 47A05
Keywords: conjugation, numerical range, antilinear, connected, path-connected, Banach space 
Muneo Chō; Injo Hur; Ji Eun Lee. Numerical ranges of conjugations and antilinear operators on a Banach space. Filomat, Tome 35 (2021) no. 8, p. 2715 . doi: 10.2298/FIL2108715C
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     title = {Numerical ranges of conjugations and antilinear operators on a {Banach} space},
     journal = {Filomat},
     pages = {2715 },
     year = {2021},
     volume = {35},
     number = {8},
     doi = {10.2298/FIL2108715C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2108715C/}
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