Unbounded symmetric homogeneous domains in spaces of operators

Lawrence A. Harris

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1995)

  • Volume: 22, Issue: 3, page 449-467
  • ISSN: 0391-173X

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Harris, Lawrence A.. "Unbounded symmetric homogeneous domains in spaces of operators." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 22.3 (1995): 449-467. <http://eudml.org/doc/84212>.

@article{Harris1995,
author = {Harris, Lawrence A.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {infinite-dimensional holomorphy; symmetric and homogeneous domains in spaces of operators; Banach space of bounded linear operators; operator norm; connected component; linear fractional transformation; Liouville's theorem},
language = {eng},
number = {3},
pages = {449-467},
publisher = {Scuola normale superiore},
title = {Unbounded symmetric homogeneous domains in spaces of operators},
url = {http://eudml.org/doc/84212},
volume = {22},
year = {1995},
}

TY - JOUR
AU - Harris, Lawrence A.
TI - Unbounded symmetric homogeneous domains in spaces of operators
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1995
PB - Scuola normale superiore
VL - 22
IS - 3
SP - 449
EP - 467
LA - eng
KW - infinite-dimensional holomorphy; symmetric and homogeneous domains in spaces of operators; Banach space of bounded linear operators; operator norm; connected component; linear fractional transformation; Liouville's theorem
UR - http://eudml.org/doc/84212
ER -

References

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  1. [1] D. Alpay - A. Duksma - J. Van Der Ploeg - H.S.V. De Snoo, Holomorphic operators between Krein spaces and the number of squares of associated kernels, in Operator Theory and Complex Analysis, T. Ando and I. Gohberg, eds., Operator Theory: Advances and Applications, Vol. 59, Birkhäuser Verlag, Basel, 1992, pp. 11-29. Zbl0790.47028MR1246808
  2. [2] J. Arazy - B. Solel, Isometries of non-self-adjoint operator algebras, J. Funct. Anal.90 (1990), 284-305. Zbl0713.46043MR1052336
  3. [3] J.A. Ball - I. Gohberg - L. Rodman, Interpolation of Rational Matrix Functions, Operator Theory: Advances and Applications, Vol. 45, Birkhäuser Verlag, Basel, 1990. Zbl0708.15011MR1083145
  4. [4] E. Ligocka - J. Siciak, Weak analytic continuation, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.20 (1972), p. 461-466. Zbl0241.46013MR317349
  5. [5] R.G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc.17 (1966), 413-415. Zbl0146.12503MR203464
  6. [6] R.G. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972. Zbl0247.47001MR361893
  7. [7] T. Franzoni, The group of holomorphic automorphisms in certain J*-algebras, Ann. Mat. Pura Appl.127 (1981), 51-66. Zbl0483.46051MR633394
  8. [8] I. Gohberg - S. Goldberg - M. Kaashoek, Classes of Linear Operators Vol. I, Operator Theory: Advances and Applications, Vol. 49, Birkhäuser Verlag, Basel, 1990. Zbl0745.47002MR1130394
  9. [9] L.A. Harris, Schwarz's lemma in normed linear spaces, Proc. Nat. Acad. Sci. U.S.A.62 (1969), 1014-1017. Zbl0199.19401MR275179
  10. [10] L.A. Harris, Bounded symmetric homogeneous domains in infinite dimensional spaces, in Infinite Dimensional Holomorphy, T.L. Hayden and T.J. Suffridge, eds., Lecture Notes in Mathematics, Vol 364, p. 13-40, Springer Verlag, Berlin, 1973. Zbl0293.46049MR407330
  11. [11] L.A. Harris, Operator Siegel domains, Proc. Royal Soc. Edinburgh Sect.79A (1977), 137-156. Zbl0376.32027MR484600
  12. [12] L.A. Harris, Schwarz-Pick systems of pseudometrics for domains in normed linear spaces, in Advances in Holomorphy, J. A. Barroso, ed., North-Holland, Amsterdam, 1979, pp. 345-406. Zbl0409.46053MR520667
  13. [13] L.A. Harris, A generalization of C*-algebras, Proc. London Math. Soc.42 (1981), 331-361. Zbl0476.46054MR607306
  14. [14] L.A. Harris, Linear fractional transformations of circular domains in operator spaces, Indiana Univ. Math. J.41 (1992), 125-147. Zbl0760.47018MR1160906
  15. [15] L.A. Harris, Factorizations of operator matrices, Linear Algebra Appl., to appear. Zbl0845.47012MR1341068
  16. [16] E. Hille, Analytic Function Theory, Vol. I, Blaisdell, New York, 1959. Zbl0088.05204
  17. [17] E. Hille - R.S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc. Colloq. Publ., Vol. 31, AMS, Providence, 1957. Zbl0078.10004MR89373
  18. [18] Loo-Keng Hua, Geometries of matrices. II. Study of involutions in the geometry of symmetric matrices, Trans. Amer. Math. Soc.61 (1947), 193-228. Zbl0037.00701MR22203
  19. [ 19] Loo-Keng Hua, Geometries of matrices. III. Fundamental theorems in the geometries of symmetric matrices, Trans. Amer. Math. Soc.61 (1947), 229-255. Zbl0037.39205MR22204
  20. [20] J.M. Isidro - L.L. Stachó, Holomorphic Automorphism Groups in Banach Spaces: An Elementary Introduction, Math. Studies Vol. 105, North-Holland, Amsterdam, 1985. Zbl0561.46022MR779821
  21. [21] V.P. Potapov, Linear fractional transformations of matrices, in Studies in the Theory of Operators and Their Applications (Russian), "Naukova Dumka," Kiev, 1979, pp. 75-97;English transl. in Amer. Math. Soc. Transl.138 (1988), 21-35. Zbl0649.15001MR566141
  22. [22] R.C. Penney, The structure of rational homogeneous domains in Cn, Ann. of Math.126 (1987), 389-414. Zbl0655.32027MR908151
  23. [23] J.-P. Ramis, Sous-ensembles analytiques d'une variété banachique complexe, Ergebnisse der Math. No. 53, Springer-Verlag, Berlin, 1970. Zbl0212.42802MR293126
  24. [24] A.G. Sergeev, On matrix Reinhardt and circled domains, in Several Complex Variables: Proceedings of the Mittag-Leffler Institute, 1987-1988, J. E. Fornaess, ed., Mathematical Notes38, Princeton Univ. Press, Princeton, 1993, pp. 573-586. Zbl0778.32002MR1207883
  25. [25] H. Upmeier, Symmetric Banach Manifolds and Jordan C*-Algebras, Math. Studies Vol. 104, North-Holland, Amsterdam, 1985. Zbl0561.46032MR776786
  26. [26] E. Vesentini, On the subharmonicity of the spectral radius, Boll. Un. Mat. Ital.4 (1968), 427-429. MR244766
  27. [27] J.-P. Vigué, Le groupe des automorphismes analytiques d'un domaine borné d'un espace de Banach complexe. Application aux domaines bornés symmetriques, Ann. Sci. Ecole Norm. Sup.9 (1976), 203-282. Zbl0333.32027MR430335
  28. [28] J. Winkelmann, On automorphisms of complements of analytic subsets in Cn, Math. Z.204 (1990), 117-127. Zbl0701.32014MR1048069

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