Published: 1995 Received: April 22, 1993Available on J-STAGE: October 20, 2006Accepted: -
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Date of correction: October 20, 2006Reason for correction: -Correction: CITATIONDetails: Wrong : 1) A. Connes, Une classification de facteurs de type III, Ann. Sci. École Norm. Sup., 4-ieme Sér., 6 (1973), 133-252. 2)S.P. Gudder and W. Scruggs, Unbounded representations of *-algebras, Pacific J. Math., 70 (1977), 369-382. 3) S. P. Gudder and R. L. Hudson, A noncommutative probability theory, Trans. Amer. Math. Soc., 245 (1978), 1-41. 4) A. Inoue, On a class of unbounded operator algebras, Pacific J. Math., 65 (1976), 77-95. 5) A, Inoue, An unbounded generalization of the Tomita-Takesaki theory I, II, Publ. Res. Inst. Math, Soc., Kyoto Univ., 22 (1986), 725-765: Publ. Res. Inst. Math. Soc., Kyoto Univ., 23 (1987), 673-726. 6) A. Inoue, Modular structure of algebras of unbounded operators, Math. Proc. Cambridge Philos. Soc., 111 (1992), 369-386. 7) A. Inoue and W. Karwowski, Cyclic generalized vectors for algebras of unbounded operators, Publ. Res. Inst. Math. Soc., Kyoto Univ., 30 (1994), 577-601. 8) A. Inoue, O*-algebras in standard system, to appear in Math. Nachr. 9) K. Katavolos and I. Koch, Extension of Tomita-Takesaki theory to the unbounded algebra of the canonical commutation relations, Rep. Math. Phys., 16 (1979), 335-352. 10) K. Kurose and H. Ogi, On a generalization of the Tomita-Takesaki theorem for a quasifree state on a self-dual CCR-algebra, Nihonkai Math. J., 1 (1990), 19-42. 11) G. Lassner, Topological algebras of operators, Rep. Math. Phys., 3 (1972), 279-293. 12) G. Pedersen and M. Takesaki, The Radon-Nikodym theorem for von Neumann algebra, Acta Math., 130 (1973), 53-88. 13) R. T. Powers, Self-adjoint algebras of unbounded operators, Comm. Math. Phys., 21 (1971), 85-124. 14) M. A. Rieffel and A. Van Daele, A bounded operator approach to Tomita-Takesaki theory, Pacific J. Math., 69 (1977), 187-221. 15) K. Schmüdgen, Unbounded Operator Algebras and Representation Theory, Akademie-Verlag, Berlin, 1990. 16) S. Stratila and L. Zsido, Lectures on von Neumann algebras, Abacus Press, Tunbridge Wells, 1979. 17) S. Stratila, Modular Theory in Operator Algebras, Abacus Press, Tunbridge Wells, 1981.
Right : [1] A. Connes, Une classification de facteurs de type III, Ann. Sci. École Norm. Sup., 4-ieme Sér., 6 (1973), 133-252. [2] S. P. Gudder and W. Scruggs, Unbounded representations of *-algebras, Pacific J. Math., 70 (1977), 369-382. [3] S. P. Gudder and R. L. Hudson, A noncommutative probability theory, Trans. Amer. Math. Soc., 245 (1978), 1-41. [4] A. Inoue, On a class of unbounded operator algebras, Pacific J. Math., 65 (1976), 77-95. [5] A, Inoue, An unbounded generalization of the Tomita-Takesaki theory I, II, Publ. Res. Inst. Math, Soc., Kyoto Univ., 22 (1986), 725-765: Publ. Res. Inst. Math, Soc., Kyoto Univ., 23 (1987), 673-726. [6] A. Inoue, Modular structure of algebras of unbounded operators, Math. Proc. Cambridge Philos. Soc., 111 (1992), 369-386. [7] A. Inoue and W. Karwowski, Cyclic generalized vectors for algebras of unbounded operators, Publ. Res. Inst. Math. Soc., Kyoto Univ., 30 (1994), 577-601. [8] A. Inoue, O*-algebras in standard system, to appear in Math. Nachr.. [9] K. Katavolos and I. Koch, Extension of Tomita-Takesaki theory to the unbounded algebra of the canonical commutation relations, Rep. Math. Phys., 16 (1979), 335-352. [10] K. Kurose and H. Ogi, On a generalization of the Tomita-Takesaki theorem for a quasifree state on a self-dual CCR-algebra, Nihonkai Math. J., 1 (1990), 19-42. [11] G. Lassner, Topological algebras of operators, Rep. Math. Phys., 3 (1972), 279-293. [12] G. Pedersen and M. Takesaki, The Radon-Nikodym theorem for von Neumann algebra, Acta Math., 130 (1973), 53-88. [13] R. T. Powers, Self-adjoint algebras of unbounded operators, Comm. Math. Phys., 21 (1971), 85-124. [14] M. A. Rieffel and A. Van Daele, A bounded operator approach to Tomita-Takesaki theory, Pacific J. Math., 69 (1977), 187-221. [15] K. Schmüdgen, Unbounded Operator Algebras and Representation Theory, Akademie-Verlag, Berlin, 1990. [16] S. Stratila and L. Zsido, Lectures on von Neumann algebras, Abacus Press, Tunbridge Wells, 1979. [17] S. Stratila, Modular Theory in Operator Algebras, Abacus Press, Tunbridge Wells, 1981.
Date of correction: October 20, 2006Reason for correction: -Correction: PDF FILEDetails: -