On embedding of -algebras

Author:
Diane Laison

Journal:
Proc. Amer. Math. Soc. **35** (1972), 499-502

MSC:
Primary 46K99

DOI:
https://doi.org/10.1090/S0002-9939-1972-0306928-8

MathSciNet review:
0306928

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An -algebra *N* with a separating family of completely additive states and with a family of mutually orthogonal projections such that and is a -algebra for each is shown to have a faithful representation as a ring of operators. This gives a new and considerably shorter proof that a semifinite -algebra with a separating family of completely additive states has a faithful representation as a ring of operators.

**[1]**J. Dixmier,*Sur certains espaces considérés par M. H. Stone*, Summa Brasil. Math.**2**(1951), 151-182. MR**14**, 69. MR**0048787 (14:69e)****[2]**J. Feldman,*Embedding of*-*algebras*, Duke Math. J.**23**(1956), 303-307. MR**17**, 1229. MR**0078669 (17:1229a)****[3]**I. Kaplansky,*Projections in Banach algebras*, Ann. of Math. (2)**53**(1951), 235-249. MR**13**, 48. MR**0042067 (13:48b)****[4]**K. Saitô,*Non-commutative extension of Lusin's theorem*, Tôhoku Math. J.**19**(1967), 332-340. MR**37**#2007. MR**0226417 (37:2007)****[5]**-,*A non-commutative theory of integration for a semi-finite*-*algebra and a problem of Feldman*, Tôhoku Math. J.**22**(1970), 420-461. MR**0275182 (43:939)****[6]**S. Sakai, -*algebras and*-*algebras*, Springer-Verlag, New York, 1971. MR**0442701 (56:1082)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
46K99

Retrieve articles in all journals with MSC: 46K99

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0306928-8

Article copyright:
© Copyright 1972
American Mathematical Society