A special version of the Schwarz lemma on an infinite dimensional domain

Tatsuhiro Honda

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1997)

  • Volume: 8, Issue: 2, page 107-110
  • ISSN: 1120-6330

Abstract

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Let B be the open unit ball of a Banach space E , and let f : B → B be a holomorphic map with f ⁢ 0 = 0 . In this paper, we discuss a condition whereby f is a linear isometry on E .

How to cite

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Honda, Tatsuhiro. "A special version of the Schwarz lemma on an infinite dimensional domain." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 8.2 (1997): 107-110. <http://eudml.org/doc/244249>.

@article{Honda1997,
abstract = { Let \( B \) be the open unit ball of a Banach space \( E \), and let \( f : B \rightarrow B \) be a holomorphic map with \( f(0) = 0 \). In this paper, we discuss a condition whereby \( f \) is a linear isometry on \( E \).},
author = {Honda, Tatsuhiro},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Banach space; Schwarz lemma; Complex geodesic; Projective space; infinite-dimensional domain; isometry},
language = {eng},
month = {7},
number = {2},
pages = {107-110},
publisher = {Accademia Nazionale dei Lincei},
title = {A special version of the Schwarz lemma on an infinite dimensional domain},
url = {http://eudml.org/doc/244249},
volume = {8},
year = {1997},
}

TY - JOUR
AU - Honda, Tatsuhiro
TI - A special version of the Schwarz lemma on an infinite dimensional domain
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1997/7//
PB - Accademia Nazionale dei Lincei
VL - 8
IS - 2
SP - 107
EP - 110
AB - Let \( B \) be the open unit ball of a Banach space \( E \), and let \( f : B \rightarrow B \) be a holomorphic map with \( f(0) = 0 \). In this paper, we discuss a condition whereby \( f \) is a linear isometry on \( E \).
LA - eng
KW - Banach space; Schwarz lemma; Complex geodesic; Projective space; infinite-dimensional domain; isometry
UR - http://eudml.org/doc/244249
ER -

References

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  2. DINEEN, S., Complex Analysis in Locally Convex Spaces. North-HollandMath. Studies, 57, 1981. Zbl0484.46044MR640093
  3. DINEEN, S., The Schwarz Lemma. Oxford Mathematical Monographs, 1989. Zbl0708.46046MR1033739
  4. DINEEN, S. - TIMONEY, R. M., Complex Geodesics on Convex Domains. Progress in Functional Analysis, 1992, 333-365. Zbl0785.46044MR1150757DOI10.1016/S0304-0208(08)70330-X
  5. DINEEN, S. - TIMONEY, R. M. - VIGUÉ, J. P., Pseudodistances invariantes sur les domaines d'un espace localement convexe. Ann. Scuola Norm. Sup. Pisa, 12, 1985, 515-529. Zbl0603.46052MR848840
  6. FRANZONI, T. - VESENTINI, E., Holomorphic Maps and Invariant Distances. North-HollandMath. Studies, 40, 1980. Zbl0447.46040MR563329
  7. JARNICKI, M. - PFLUG, P., Invariant Distances and Metrics in Complex Analysis, de Gruyter, Berlin-New York1983. Zbl0789.32001MR1242120DOI10.1515/9783110870312
  8. HAMADA, H., A Schwarz lemma in several complex variables. In: Proceedings of the Third International Colloquium on Finite or Infinite Dimensional Complex Analysis. Seoul, Korea, 1995, 105-110. 
  9. NISHIHARA, M., On the indicator of growth of entire functions of exponential type in infinite dimensional spaces and the Levi problem in infinite dimensional projective spaces. Portugaliae Math., 52, 1995, 61-94. Zbl0935.32003MR1324083
  10. VESENTINI, E., Variations on a theme of Carathéodory. Ann. Scuola Norm. Sup. Pisa, 7 (4), 1979, 39-68. Zbl0413.46039MR529475
  11. VESENTINI, E., Complex geodesics. Compositio Math., 44, 1981, 375-394. Zbl0488.30015MR662466
  12. VESENTINI, E., Complex geodesics and holomorphic maps. Sympos. Math., 26, 1982, 211-230. Zbl0506.32008MR663034
  13. VIGUÉ, J. P., Un lemme de Schwarz pour les domaines bornés symétriques irréductibles et certains domaines bornés strictement convexes. Indiana Univ. Math. J., 40, 1991, 239-304. Zbl0733.32025
  14. VIGUÉ, J. P., Le lemme de Schwarz et la caractérisation des automorphismes analytiques. Astérisque, 217, 1993, 241-249. Zbl0798.32023

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