Tohoku Mathematical Journal

Conditional expectation in an operator algebra, II

Hisaharu Umegaki

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 8, Number 1 (1956), 86-100.

Dates
First available in Project Euclid: 4 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178245011

Digital Object Identifier
doi:10.2748/tmj/1178245011

Mathematical Reviews number (MathSciNet)
MR0090789

Zentralblatt MATH identifier
0072.12501

Subjects
Primary: 46.2X

Citation

Umegaki, Hisaharu. Conditional expectation in an operator algebra, II. Tohoku Math. J. (2) 8 (1956), no. 1, 86--100. doi:10.2748/tmj/1178245011. https://projecteuclid.org/euclid.tmj/1178245011


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References

  • [1] R R BAHADUR, Measurable subspaces and subalgebras, Proc. of Amer. Math. Soc., 6 (1955), 565-670.
  • [2] J DIXMIER, Formes lineaires sur un anneau d'operateurs, Bull, de la Soc. Math de France (1953), 6-39.
  • [3] J. L DOOB, Stochastic processes, New York, 1953
  • [4] HA. DYE, The Randon-Nikodym theorem for finite rings of operators, Trans Amer. Math Soc, 72(1952), 234-280.
  • [5] E. L GRIFFIN, Some contributions to the theory of rings of operators, Trans Amer. Math. Soc., 76(1954), 471-504.
  • [6] I. KAPLANSKY, A theorem on rings of operators, Pacific. Journ. of Math., 1(1951), 227-232.
  • [7] S C. MOY, Characterizations of.conditional expectation as a transformation o function spaces, Pacific Journ. of Math., 4(1954), 47-65.
  • [8] M. NAKAMURA AND T. TURUMARU, Expectations in an operator algebra, Thok Math. Journ, 6(1954), 182-188.
  • [9] J VON NEUMANN, On rings operators, III, Ann. of Math., 41(1949), 94-161
  • [10] I. E. SEGAL, A non-commutative extension of abstract integration, Ann. o Math., 57(1953), 401-457.
  • [11] H. UMEGAKI, Conditional expectation in an operator algebra, Thoku Mat Journ., 6(1954), 177-181.

See also

  • Original Paper: Hisaharu Umegaki. Conditional expectation in an operator algebra, I. Tohoku Math. J., Volume 6, Number 2-3 (1954), pp. 177-181.