Carathéodory balls and norm balls in $H_{p,n} = {z ∈ ℂ^{n} :∥z∥ _{p} < 1}$

Schwarz, Binyamin; Srebro, Uri

Carathéodory balls and norm balls in

H_{p, n} = z \in ℂ^{n} : ∥ z ∥_{p} < 1

Schwarz, Binyamin ; Srebro, Uri

Banach Center Publications, Tome 37 (1996), p. 75-83 / Harvested from The Polish Digital Mathematics Library

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Résumé

It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on $H_{p, n} = z \in ℂ^{n} : ∥ z ∥_{p} < 1$ which are balls with respect to the complex $l_{p}$ norm in $ℂ^{n}$ are those centered at the origin.

Publié le : 1996-01-01

Zbl 0873.32027

EUDML-ID : urn:eudml:doc:208619

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     author = {Schwarz, Binyamin and Srebro, Uri},
     title = {Caratheodory balls and norm balls in $H\_{p,n} = {z [?] C^{n} :[?]z[?] \_{p} < 1}$
            },
     journal = {Banach Center Publications},
     volume = {37},
     year = {1996},
     pages = {75-83},
     zbl = {0873.32027},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv37i1p75bwm}
}

Schwarz, Binyamin; Srebro, Uri. Carathéodory balls and norm balls in $H_{p,n} = {z ∈ ℂ^{n} :∥z∥ _{p} < 1}$
            . Banach Center Publications, Tome 37 (1996) pp. 75-83. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv37i1p75bwm/

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