Holomorphic automorphisms of the unit ball of a direct sum

Carlo Petronio

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1990)

  • Volume: 1, Issue: 3, page 203-213
  • ISSN: 1120-6330

Abstract

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We endow the direct sum of two complex Banach spaces with a suitable norm, and we investigate the orbit of the origin for the group of holomorphic automorphisms of the outcoming unit ball.

How to cite

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Petronio, Carlo. "Holomorphic automorphisms of the unit ball of a direct sum." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.3 (1990): 203-213. <http://eudml.org/doc/244154>.

@article{Petronio1990,
abstract = {We endow the direct sum of two complex Banach spaces with a suitable norm, and we investigate the orbit of the origin for the group of holomorphic automorphisms of the outcoming unit ball.},
author = {Petronio, Carlo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Direct sum; p-norm; Orbit of the origin; biholomorphic automorphisms},
language = {eng},
month = {9},
number = {3},
pages = {203-213},
publisher = {Accademia Nazionale dei Lincei},
title = {Holomorphic automorphisms of the unit ball of a direct sum},
url = {http://eudml.org/doc/244154},
volume = {1},
year = {1990},
}

TY - JOUR
AU - Petronio, Carlo
TI - Holomorphic automorphisms of the unit ball of a direct sum
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/9//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 3
SP - 203
EP - 213
AB - We endow the direct sum of two complex Banach spaces with a suitable norm, and we investigate the orbit of the origin for the group of holomorphic automorphisms of the outcoming unit ball.
LA - eng
KW - Direct sum; p-norm; Orbit of the origin; biholomorphic automorphisms
UR - http://eudml.org/doc/244154
ER -

References

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  1. BRAUN, R. - KAUP, W. - UPMEIER, H., On the automorphisms of circular and Reinhardt domains in complex Banach spaces. Manuscripta Math., 25, 1978, 97-133. Zbl0398.32001MR500878DOI10.1007/BF01168604
  2. DORAN, S. - BELFI, A., Characterizations of C * -algebras. Lect. Notes in Pure and Appl. Math., 101, 1986. Zbl0597.46056
  3. KAUP, W. - UPMEIER, H., Banach spaces with biholomorphically equivalent unit balls are isomorphic. Proc. Amer. Math. Soc., 58, 1976, 129-133. Zbl0337.32012MR422704
  4. KRITIKOS, N., Uber analytische Abbildungen einer Klasse von vier dimensionalen Gebieten. Math. Ann., 99, 1928, 321-341. MR1512453JFM54.0373.02
  5. PETRONIO, C., Holomorphic automorphism groups in certain compact operator spaces. Rend. Mat. Acc. Lincei, s. 9, vol. 1, fasc. 2, 1990, 125-130. Zbl0738.47031MR1081395
  6. STACHÓ, L. L., A short proof of the fact that biholomorphic automorphisms of the unit ball in certain L p spaces are linear. Acta Sci. Math., 41, 1979, 381-383. Zbl0432.58006MR555432
  7. THULLEN, P., Zu den Abbildungen durch analytische Funktionen mehrer komplexer Verandlicher. Die Invarianz des Mittelpunktes von Kreiskòrpern.Math. Ann., 104, 1931, 244-259, 373-376. Zbl0001.02303
  8. VESENTINI, E., Automorphisms of the unit ball. In: Several Complex Variables (Cortona, 1976/77)Scuola Normale Superiore, Pisa1978, 282-284. Zbl0443.32016
  9. VESENTINI, E., Variations on a theme of Carathéodory. Ann. Scuola Norm. Sup. Pisa, (4), 6, 1979, 39-68. Zbl0413.46039MR529475

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