Manifold of primitive idempotents in a Jordan-Hilbert algebra

Takaaki NOMURA

doi:10.2969/jmsj/04510037

Takaaki NOMURA

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1993 年 45 巻 1 号 p. 37-58

DOI https://doi.org/10.2969/jmsj/04510037

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Published: 1993 Received: 1991/12/11 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) W. Ambrose, Structure theorem for a special class of Banach algebras, Trans. Amer. Math. Soc., 57 (1945), 364-386.
2) P. de la Harpe, Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space, Lecture Notes in Math., 285, Springer, Berlin, 1972.
3) J. Faraut, Algèbres de Jordan et cones symétriques, École d'été CIMPA, 1988.
4) N. Grossman, Hilbert manifolds without epiconjugate points, Proc. Amer. Math. Soc., 16 (1965), 1365-1371.
5) L. A. Harris and W. Kaup, Linear algebraic groups in infinite dimension, Illinois J. Math., 21 (1977), 666-674.
6) U. Hirzebruch, Über Jordan-Algebren und kompakte Riemannsche symmetrische Räume vom Rang 1, Math. Z., 90 (1965), 339-354.
7) T. Kato, Perturbation theory for linear operators, Springer, Berlin, 1966.
8) W. Kaup, Über die Klassifikation der symmetrischen hermiteschen Mannigfaltigkeiten unendlicher Dimension I, Math. Ann., 257 (1981), 463-486; II, Math. Ann., 262 (1983), 57-75.
9) W. Klingenberg, Riemannian geometry, Walter de Gruyter, Berlin, 1982.
10) E. Määttä, On the Frenet theory of plane fields in Hilbert space, Ann. Acad. Sci. Fenn., Dissert., 47 (1983).
11) K. McCrimmon, Peirce ideals in Jordan algebras, Pacific J. Math., 78 (1978), 397-414.
12) E. Neher, Jordan triple systems by the grid approach, Lecture Notes in Math., 1280, Springer, Berlin, 1987.
13) H. Porta and L. Recht, Minimality of geodesics in Grassmann manifolds, Proc. Amer. Math. Soc., 100 (1987), 464-466.
14) H. Upmeier, Automorphism groups of Jordan C^*-algebras, Math. Z., 176 (1981), 21-34.
15) H. Upmeier, Symmetric Banach manifolds and Jordan C^*-algebras, North-Holland, Amsterdam, 1985.
16) C. Viola Devapakkiam, Hilbert space methods in the theory of Jordan algebras I, Math. Proc. Cambridge Philos. Soc., 78 (1974), 293-300.

Right : [1] W. Ambrose, Structure theorem for a special class of Banach algebras, Trans. Amer. Math. Soc., 57 (1945), 364-386.
[2] P. de la Harpe, Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space, Lecture Notes in Math., 285, Springer, Berlin, 1972.
[3] J. Faraut, Algèbres de Jordan et cônes symétriques, École d'été CIMPA, 1988.
[4] N. Grossman, Hilbert manifolds without epiconjugate points, Proc. Amer. Math. Soc., 16 (1965), 1365-1371.
[5] L. A. Harris and W. Kaup, Linear algebraic groups in infinite dimension, Illinois J. Math., 21 (1977), 666-674.
[6] U. Hirzebruch, Über Jordan-Algebren und kompakte Riemannsche symmetrische Räume vom Rang 1, Math. Z., 90 (1965), 339-354.
[7] T. Kato, Perturbation theory for linear operators, Springer, Berlin, 1966.
[8] W. Kaup, Über die Klassifikation der symmetrischen hermiteschen Mannigfaltigkeiten unendlicher Dimension I, Math. Ann., 257 (1981), 463-486; II, Math. Ann., 262 (1983), 57-75.
[9] W. Klingenberg, Riemannian geometry, Walter de Gruyter, Berlin, 1982.
[10] E. Määttä, On the Frenet theory of plane fields in Hilbert space, Ann. Acad. Sci. Fenn., Dissert., 47 (1983).
[11] K. McCrimmon, Peirce ideals in Jordan algebras, Pacific J. Math., 78 (1978), 397-414.
[12] E. Neher, Jordan triple systems by the grid approach, Lecture Notes in Math., 1280, Springer, Berlin, 1987.
[13] H. Porta and L. Recht, Minimality of geodesics in Grassmann manifolds, Proc. Amer. Math. Soc., 100 (1987), 464-466.
[14] H. Upmeier, Automorphism groups of Jordan C-algebras, Math. Z., 176 (1981), 21-34.
[15] H. Upmeier, Symmetric Banach manifolds and Jordan C-algebras, North-Holland, Amsterdam, 1985.
[16] C. Viola Devapakkiam, Hilbert space methods in the theory of Jordan algebras I, Math. Proc. Cambridge Philos. Soc., 78 (1974), 293-300.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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