Regular embeddings of C*-algebras in monotone complete C*-algebras

Masamichi HAMANA

doi:10.2969/jmsj/03310159

Regular embeddings of C^*-algebras in monotone complete C^*-algebras

Masamichi HAMANA

Author information

JOURNAL FREE ACCESS

1981 Volume 33 Issue 1 Pages 159-183

DOI https://doi.org/10.2969/jmsj/03310159

Details

Published: 1981 Received: November 27, 1978 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. K. Berberian, Baer *-rings, Springer-Verlag, Berlin, 1972.
2) M.-D. Choi and E.G. Effros, The completely positive lifting problem for C^*-algebras, Ann. of Math., 104 (1976), 585-609.
3) M.-D. Choi and E.G. Effros, Injectivity and operator spaces, J. Functional Analysis, 24 (1977), 156-209.
4) H.B. Cohen, Injective envelopes of Banach spaces, Bull. Amer. Math. Soc., 70 (1964), 723-726.
5) E.G. Effros, Aspects of noncommutative order, Notes for a lecture given at The Second U.S. Japan Seminar on C^*-algebras and Applications to Physics, April 1977.
6) M. Hamana, Injective envelopes of C^*-algebras, J. Math. Soc. Japan., 31 (1979), 181-197.
7) J.R. Isbell, Three remarks on injective envelopes of Banach spaces, J. Math. Anal. Appl., 27 (1969), 516-518.
8) R.V. Kadison, Operator algebras with a faithful weakly-closed representation, Ann. of Math., 64 (1956), 175-181.
9) R.V. Kadison, Unitary invariants for representations of operator algebras, Ann. of Math., 66 (1957), 304-379.
10) R.V. Kadison and G.K. Pedersen, Equivalence in operator algebras, Math. Stand., 27 (1970), 205-222.
11) I. Kaplansky, Projections in Banach algebras, Ann. of Math., 53 (1951), 235-249.
12) I. Kaplansky, Group algebras in the large, Tohoku Math. J., 3 (1951), 249-256.
13) I. Kaplansky, Algebras of type I, Ann. of Math., 56 (1952), 460-472.
14) R. Kaufman, A type of extension of Banach spaces, Acta Sci. Math. (Szeged), 27 (1966), 163-166.
15) H.E. Lacey, The isometric theory of classical Banach spaces, Springer-Verlag, Berlin, 1974.
16) G.K. Pedersen, On weak and monotone σ-closure of C^*-algebras, Commun. Math. Phys., 11 (1969), 221-226.
17) K. Saito, On the embedding as a double commutator in a type I AW^*-algebras II, Tohoku Math. J., 26 (1974), 333-339.
18) M. Takesaki, A note on the cross-norm of the direct product of operator algebra, Kodai Math. Sem. Rep., 10 (1958), 137-140.
19) J. Tomiyama, On the product projection of norm one in the direct product of operator algebras, Tohoku Math. J., 11 (1959), 305-313.
20) J. Tomiyama, Tensor products and projections of norm one in von Neumann algebras, Lecture Notes, Univ. of Copenhagen, 1970.
21) J.D.M. Wright, Embedding in vector lattices, J. London Math. Soc. (2), 8 (1974), 699-706.
22) J.D.M. Wright, Regular σ-completions of C^*-algebras, J. London Math. Soc. (2), 12 (1976), 299-309.
23) J.D.M. Wright, Wild AW^*-factors and Kaplansky-Rickart algebras, J. London Math. Soc. (2), 13 (1976), 83-89.

Right : [1] S. K. Berberian, Baer *-rings, Springer-Verlag, Berlin, 1972.
[2] M. -D. Choi and E. G. Effros, The completely positive lifting problem for C-algebras, Ann. of Math., 104 (1976), 585-609.
[3] M. -D. Choi and E. G. Effros, Injectivity and operator spaces, J. Functional Analysis, 24 (1977), 156-209.
[4] H. B. Cohen, Injective envelopes of Banach spaces, Bull. Amer. Math. Soc., 70 (1964), 723-726.
[5] E. G. Effros, Aspects of noncommutative order, Notes for a lecture given at The Second U. S. Japan Seminar on C-algebras and Applications to Physics, April 1977.
[6] M. Hamana, Injective envelopes of C-algebras, J. Math. Soc. Japan., 31 (1979), 181-197.
[7] J. R. Isbell, Three remarks on injective envelopes of Banach spaces, J. Math. Anal. Appl., 27 (1969), 516-518.
[8] R. V. Kadison, Operator algebras with a faithful weakly-closed representation, Ann. of Math., 64 (1956), 175-181.
[9] R. V. Kadison, Unitary invariants for representations of operator algebras, Ann. of Math., 66 (1957), 304-379.
[10] R. V. Kadison and G. K. Pedersen, Equivalence in operator algebras, Math. Stand., 27 (1970), 205-222.
[11] I. Kaplansky, Projections in Banach algebras, Ann. of Math., 53 (1951), 235-249.
[12] I. Kaplansky, Group algebras in the large, Tôhoku Math. J., 3 (1951), 249-256.
[13] I. Kaplansky, Algebras of type I, Ann. of Math., 56 (1952), 460-472.
[14] R. Kaufman, A type of extension of Banach spaces, Acta Sci. Math. (Szeged), 27 (1966), 163-166.
[15] H. E. Lacey, The isometric theory of classical Banach spaces, Springer-Verlag, Berlin, 1974.
[16] G. K. Pedersen, On weak and monotone σ-closure of C-algebras, Commun. Math. Phys., 11 (1969), 221-226.
[17] K. Saitô, On the embedding as a double commutator in a type I AW-algebras II, Tôhoku Math. J., 26 (1974), 333-339.
[18] M. Takesaki, A note on the cross-norm of the direct product of operator algebra, Kodai Math. Sem. Rep., 10 (1958), 137-140.
[19] J. Tomiyama, On the product projection of norm one in the direct product of operator algebras, Tôhoku Math. J., 11 (1959), 305-313.
[20] J. Tomiyama, Tensor products and projections of norm one in von Neumann algebras, Lecture Notes, Univ. of Copenhagen, 1970.
[21] J. D. M. Wright, Embedding in vector lattices, J. London Math. Soc. (2), 8 (1974), 699-706.
[22] J. D. M. Wright, Regular σ-completions of C-algebras, J. London Math. Soc. (2), 12 (1976), 299-309.
[23] J. D. M. Wright, Wild AW-factors and Kaplansky-Rickart algebras, J. London Math. Soc. (2), 13 (1976), 83-89.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!