Holomorphic automorphism groups in certain compact operator spaces

Carlo Petronio

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

  • Volume: 1, Issue: 2, page 125-130
  • ISSN: 1120-6330

Abstract

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A class of Banach spaces of compact operators in Hilbert spaces is introduced, and the holomorphic automorphism groups of the unit balls of these spaces are investigated.

How to cite

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Petronio, Carlo. "Holomorphic automorphism groups in certain compact operator spaces." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.2 (1990): 125-130. <http://eudml.org/doc/244318>.

@article{Petronio1990,
abstract = {A class of Banach spaces of compact operators in Hilbert spaces is introduced, and the holomorphic automorphism groups of the unit balls of these spaces are investigated.},
author = {Petronio, Carlo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Compact operator; Unit ball; Isometry; Non-homogeneity; Banach spaces of complex operators in Hilbert spaces; holomorphic automorphism groups of the unit balls},
language = {eng},
month = {5},
number = {2},
pages = {125-130},
publisher = {Accademia Nazionale dei Lincei},
title = {Holomorphic automorphism groups in certain compact operator spaces},
url = {http://eudml.org/doc/244318},
volume = {1},
year = {1990},
}

TY - JOUR
AU - Petronio, Carlo
TI - Holomorphic automorphism groups in certain compact operator spaces
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/5//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 2
SP - 125
EP - 130
AB - A class of Banach spaces of compact operators in Hilbert spaces is introduced, and the holomorphic automorphism groups of the unit balls of these spaces are investigated.
LA - eng
KW - Compact operator; Unit ball; Isometry; Non-homogeneity; Banach spaces of complex operators in Hilbert spaces; holomorphic automorphism groups of the unit balls
UR - http://eudml.org/doc/244318
ER -

References

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  1. FRANZONI, T., The group of holomorphic automorphisms in certain J*-algebras. Ann. di Mat. Pura e Appl. (IV), 127, 1981, 31-66. Zbl0483.46051MR633394DOI10.1007/BF01811718
  2. FRANZONI, T. - VESENTINI, E., Holomorphic Maps and Invariant Distances. North - Holland Math. Studies, 69, 1980. Zbl0447.46040MR563329
  3. HALMOS, P. R., A Hilbert space problem book. Van Nostrand Company Inc., 1967. Zbl0144.38704MR208368
  4. HARRIS, L. A., Bounded symmetric homogeneous domains in infinite dimensional spaces. Lecture Notes in Mathematics, 364, Berlin-Heidelberg-New York, Springer1973, 13-40. Zbl0293.46049MR407330
  5. KAUP, W. - UPMEIER, H., Banach spaces with biholomorphically equivalent unit balls are isomorphic. Proc. Amer. Math. Soc, 58, 1976, 129-133. Zbl0337.32012MR422704
  6. MCCARTHY, C. A., c p . Israel J. Math., 5, 1967, 249-271. MR225140
  7. PETRONIO, C., Variazioni su un tema di Thullen: domini limitati non omogenei in spazi diBanach. (Tesi di laurea) Università degli Studi di Pisa, A.A. 1988/89. 
  8. SCHATTEN, R., A theory of cross-spaces. Princeton University Press, 1950. Zbl0041.43502MR36935
  9. SCHATTEN, R., Norm ideals of completely continuous operators. Ergebn. der Math., 27, Springer-Verlag, 1960 Zbl0090.09402MR119112
  10. STACHO, 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
  11. VESENTINI, E., Automorphisms of the unit hall. In: Several Complex Variables. Cortona, 1976/77. Scuola Normale Superiore, Pisa1978, 282-284. Zbl0443.32016
  12. VESENTINI, E., Variations on a theme of Carathéodory. Ann. Scuola Norm. Sup. Pisa, (4), 6, 1979, 39-68. Zbl0413.46039MR529475

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