Unbounded representations of symmetric *-algebras

Atsushi INOUE

doi:10.2969/jmsj/02920219

Atsushi INOUE

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1977 Volume 29 Issue 2 Pages 219-232

DOI https://doi.org/10.2969/jmsj/02920219

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Published: 1977 Received: July 08, 1975 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) G. R. Allan, On a class of locally convex algebras, Proc. London Math. Soc., (3) 17 (1967), 91-114.
2) J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gausthier-Villars, Paris, 2é edition, 1969.
3) P. G. Dixon, Generalized B*-algebras, Proc. London Math. Soc., (3) 21 (1970), 693-715.
4) P. G. Dixon, Unbounded operator algebras, Proc. London Math. Soc., (3) 23 (1971), 53-69.
5) N. Dunford and J. Schwartz, Linear operators, vol. II, Interscience Pub., New York; 1963.
6) R. Godement, Sur la théorie des représentations unitaires, Ann. of Math., (2) 53 (1951), 68-124.
7) A. Inoue, Representations of GB*-algebras I, Fukuoka Univ. Sci. Reports, 5 (1975), 63-78.
8) A. Inoue, Representations of GB*-algebras II, Fukuoka Univ. Sci. Reports, 5 (1975), 21-41.
9) A. Inoue, On a class of unbounded operator algebras, Pacific J. Math., 65 (1976), 77-95.
10) A. Inoue, On a class of unbounded operator algebras II, Pacific J. Math., (to appear).
11) A. Inoue, On a class of unbounded operator algebras III, Pacific J. Math., 69 (1977), 105-116.
12) A. Inoue, On a class of unbounded operator algebras IV, J. Math. Anal. Appl., (to appear).
13) A. Inoue, Unbounded Hilbert algebras as locally convex *-algebras, Math. Rep. Coll. General Edu. Kyushu Univ. X, (2) (1976), 114-129.
14) E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc., 11 (1952).
15) A. E. Nussbaum, On the integral representation of positive linear functionals, Trans. Amer. Math. Soc., 128 (1967), 460-473.
16) R. T. Powers, Self-adjoint algebras of unbounded operators, Commun. Math. Phys., 21 (1971), 85-124.
17) C. E. Richart, General theory of Banach algebras, Van Nostrand, Princeton, 1960.

Right : [1] G. R. Allan, On a class of locally convex algebras, Proc. London Math. Soc., (3) 17 (1967), 91-114.
[2] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gausthier-Villars, Paris, 2é edition, 1969.
[3] P. G. Dixon, Generalized B^*-algebras, Proc. London Math. Soc., (3) 21 (1970), 693-715.
[4] P. G. Dixon, Unbounded operator algebras, Proc. London Math. Soc., (3) 23 (1971), 53-69.
[5] N. Dunford and J. Schwartz, Linear operators, vol. II, Interscience Pub., New York; 1963.
[6] R. Godement, Sur la théorie des représentations unitaires, Ann. of Math., (2) 53 (1951), 68-124.
[7] A. Inoue, Representations of GB^*-algebras I, Fukuoka Univ. Sci. Reports, 5 (1975), 63-78.
[8] A. Inoue, Representations of GB^*-algebras II, Fukuoka Univ. Sci. Reports, 5 (1975), 21-41.
[9] A. Inoue, On a class of unbounded operator algebras, Pacific J. Math., 65 (1976), 77-95.
[10] A. Inoue, On a class of unbounded operator algebras II, Pacific J. Math., (to appear).
[11] A. Inoue, On a class of unbounded operator algebras III, Pacific J. Math., 69 (1977), 105-116.
[12] A. Inoue, On a class of unbounded operator algebras IV, J. Math. Anal. Appl., (to appear).
[13] A. Inoue, Unbounded Hilbert algebras as locally convex *-algebras, Math. Rep. Coll. General Edu. Kyushu Univ. X, (2) (1976), 114-129.
[14] E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc., 11 (1952).
[15] A. E. Nussbaum, On the integral representation of positive linear functionals, Trans. Amer. Math. Soc., 128 (1967), 460-473.
[16] R. T. Powers, Self-adjoint algebras of unbounded operators, Commun. Math. Phys., 21 (1971), 85-124.
[17] C. E. Richart, General theory of Banach algebras, Van Nostrand, Princeton, 1960.

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