Carathéodory balls and norm balls in H p , n = z ∈ ℂ n : ∥ z ∥ p < 1

Binyamin Schwarz; Uri Srebro

Banach Center Publications (1996)

  • Volume: 37, Issue: 1, page 75-83
  • ISSN: 0137-6934

Abstract

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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 ∈ 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.

How to cite

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Schwarz, Binyamin, and Srebro, Uri. "Carathéodory balls and norm balls in $H_{p,n} = {z ∈ ℂ^{n} :∥z∥ _{p} < 1}$." Banach Center Publications 37.1 (1996): 75-83. <http://eudml.org/doc/208619>.

@article{Schwarz1996,
abstract = {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 $H_\{p,n\} = \{z ∈ ℂ^\{n\}: ∥ z∥_\{p\} < 1 \}$ which are balls with respect to the complex $l_\{p\}$ norm in $ℂ^\{n\}$ are those centered at the origin.},
author = {Schwarz, Binyamin, Srebro, Uri},
journal = {Banach Center Publications},
keywords = {Carathéodory balls; norm balls},
language = {eng},
number = {1},
pages = {75-83},
title = {Carathéodory balls and norm balls in $H_\{p,n\} = \{z ∈ ℂ^\{n\} :∥z∥ _\{p\} < 1\}$},
url = {http://eudml.org/doc/208619},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Schwarz, Binyamin
AU - Srebro, Uri
TI - Carathéodory balls and norm balls in $H_{p,n} = {z ∈ ℂ^{n} :∥z∥ _{p} < 1}$
JO - Banach Center Publications
PY - 1996
VL - 37
IS - 1
SP - 75
EP - 83
AB - 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 $H_{p,n} = {z ∈ ℂ^{n}: ∥ z∥_{p} < 1 }$ which are balls with respect to the complex $l_{p}$ norm in $ℂ^{n}$ are those centered at the origin.
LA - eng
KW - Carathéodory balls; norm balls
UR - http://eudml.org/doc/208619
ER -

References

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  1. [D] S. Dineen, The Schwarz lemma, Oxford Mathematical Monograph, Clarendon Press, 1989. Zbl0708.46046
  2. [JP] M. Jarnicki and P. Pflug, Invariant distances and metrics in complex analysis, Walter de Gruyter, 1993. Zbl0789.32001
  3. [JPZ] M. Jarnicki, P. Pflug and R. Zeinstra, Geodesics for convex complex ellipsoids, Annali d. Scuola Normale Superiore di Pisa XX Fasc. 4 (1993), 535-543. Zbl0812.32010
  4. [R] W. Rudin, Function theory in the unit ball of ℂ n , Springer, New York, 1980. Zbl0495.32001
  5. [Sch] B. Schwarz, Carathéodory balls and norm balls of the domain H = ( z 1 , z 2 ) ∈ ℂ 2 : | z 1 | + | z 2 | < 1 , Israel J. of Math. 84 (1993), 119-128. 
  6. [Sr] U. Srebro, Carathéodory balls and norm balls in H = z ∈ ℂ n : ∥ z ∥ 1 < 1 , Israel J. Math. 89 (1995), 61-70. 
  7. [Z] W. Zwonek, Carathéodory balls and norm balls of the domains H n = z ∈ ℂ n : | z 1 | + . . . + | z n | < 1 , Israel J. Math. 89 (1995), 71-76. Zbl0824.32007

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