Tohoku Mathematical Journal

On the algebra of measurable operators for a general ${\rm AW}^{\ast}$-algebra

Kazuyuki Saitô

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 21, Number 2 (1969), 249-270.

Dates
First available in Project Euclid: 4 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178242995

Digital Object Identifier
doi:10.2748/tmj/1178242995

Mathematical Reviews number (MathSciNet)
MR0247493

Zentralblatt MATH identifier
0183.14302

Subjects
Primary: 46.65
Secondary: 16.00

Citation

Saitô, Kazuyuki. On the algebra of measurable operators for a general ${\rm AW}^{\ast}$-algebra. Tohoku Math. J. (2) 21 (1969), no. 2, 249--270. doi:10.2748/tmj/1178242995. https://projecteuclid.org/euclid.tmj/1178242995


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References

  • [1] S. K. BERBERIAN, The regular ring of a finite.AT^-algebra, Ann. of Math., 65(1957), 224-240.
  • [2] J. DIXMIER, Sur certains espaces consideres par M. H. Stone, Summa Brasil. Math., 2(1951), 151-182.
  • [3] I. KAPLANSKY, Projections in Banach algebras Ann. of Math., 53(1951), 235-249
  • [4] I. KAPLANSKY, Algebras of type I, Ann. of Math., 56(1952), 460-472
  • [5] I. KAPLANSKY, Any orthocomplementedcomplete modular lattice is a continuou geometry, Ann. of Math., 61(1955), 524-541.
  • [6] I. KAPLANSKY, Rings of operators (Note prepared by S. K. Berberian with an appendi by R. Blattner), Univ. of Chicago Notes, 1955.
  • [7] T. OGASAWARA AND K. YOSHINAGA, A non-commutative theory of integration fo operators, J. Sci. Hiroshima, 18(1955), 311-347.
  • [8] S. SAKAI, The theory of Wr*-algebras, Mimeographed note, Yale Univ., 1962
  • [9] I. E. SEGAL, A non-commutative extension of abstract integration, Ann. of Math., 57(1953), 401-457.
  • [10] J. VON. NEUMANN, Continuous geometry, Princeton, 1960
  • [11] Ti Yen, Trace on finite AW*-algebras, Duke Math. J., 22(1955), 207-222

See also

  • Part II: Kazuyuki Saitô. On the algebra of measurable operators for a general $AW^{\ast}$-algebra, II. Tohoku Math. J., Volume 23, Number 3 (1971), pp. 525-534.