Subhomogeneous AF $C^ \ast$-algebras and their Fubini products
HTML articles powered by AMS MathViewer
- by Seung-Hyeok Kye
- Proc. Amer. Math. Soc. 94 (1985), 249-253
- DOI: https://doi.org/10.1090/S0002-9939-1985-0784173-9
- PDF | Request permission
Abstract:
We give a characterization of subhomogeneous AF ${C^ * }$-algebras in terms of their ${C^*}$-subalgebras. Also, we show that an AF ${C^*}$-algebra is a ${C^*}$-algebra with trivial Fubini products if and only if it is subhomogeneous.References
- R. J. Archbold and C. J. K. Batty, $C^{\ast }$-tensor norms and slice maps, J. London Math. Soc. (2) 22 (1980), no. 1, 127–138. MR 579816, DOI 10.1112/jlms/s2-22.1.127
- C. J. K. Batty, Derivations of tensor products of $C^*$-algebras, J. London Math. Soc. (2) 17 (1978), no. 1, 129–140. MR 477788, DOI 10.1112/jlms/s2-17.1.129
- Ola Bratteli, Inductive limits of finite dimensional $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 171 (1972), 195–234. MR 312282, DOI 10.1090/S0002-9947-1972-0312282-2
- Joel M. Cohen, $C^{\ast }$-algebras without idempotents, J. Functional Analysis 33 (1979), no. 2, 211–216. MR 546507, DOI 10.1016/0022-1236(79)90112-5
- J. M. G. Fell, The structure of algebras of operator fields, Acta Math. 106 (1961), 233–280. MR 164248, DOI 10.1007/BF02545788
- James Glimm, Type I $C^{\ast }$-algebras, Ann. of Math. (2) 73 (1961), 572–612. MR 124756, DOI 10.2307/1970319
- Tadasi Huruya, Fubini products of $C^{\ast }$-algebras, Tohoku Math. J. (2) 32 (1980), no. 1, 63–70. MR 567831, DOI 10.2748/tmj/1178229682
- Tadasi Huruya, On compact completely bounded maps of $C^{\ast }$-algebras, Michigan Math. J. 30 (1983), no. 2, 213–220. MR 718267, DOI 10.1307/mmj/1029002852
- Tadasi Huruya and Jun Tomiyama, Completely bounded maps of $C^{\ast }$-algebras, J. Operator Theory 10 (1983), no. 1, 141–152. MR 715564
- Aldo J. Lazar, On some elementary properties of AF algebras, Indiana Univ. Math. J. 30 (1981), no. 3, 433–439. MR 611231, DOI 10.1512/iumj.1981.30.30034
- A. J. Lazar and D. C. Taylor, Approximately finite-dimensional $C^{\ast }$-algebras and Bratteli diagrams, Trans. Amer. Math. Soc. 259 (1980), no. 2, 599–619. MR 567100, DOI 10.1090/S0002-9947-1980-0567100-9
- Gert K. Pedersen, $C^{\ast }$-algebras and their automorphism groups, London Mathematical Society Monographs, vol. 14, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1979. MR 548006
- Gert K. Pedersen, The linear span of projections in simple $C^{\ast }$-algebras, J. Operator Theory 4 (1980), no. 2, 289–296. MR 595417
- R. R. Smith, Completely bounded maps between $C^{\ast }$-algebras, J. London Math. Soc. (2) 27 (1983), no. 1, 157–166. MR 686514, DOI 10.1112/jlms/s2-27.1.157
- Jun Tomiyama, Tensor products and approximation problems of $C^*$-algebras, Publ. Res. Inst. Math. Sci. 11 (1975/76), no. 1, 163–183. MR 0397427, DOI 10.2977/prims/1195191690
- Jun Tomiyama, On the difference of $n$-positivity and complete positivity in $C^{\ast }$-algebras, J. Functional Analysis 49 (1982), no. 1, 1–9. MR 680854, DOI 10.1016/0022-1236(82)90083-0
- Simon Wassermann, On tensor products of certain group $C^{\ast }$-algebras, J. Functional Analysis 23 (1976), no. 3, 239–254. MR 0425628, DOI 10.1016/0022-1236(76)90050-1
- Simon Wassermann, A pathology in the ideal space of $L(H)\otimes L(H)$, Indiana Univ. Math. J. 27 (1978), no. 6, 1011–1020. MR 511255, DOI 10.1512/iumj.1978.27.27069
Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 249-253
- MSC: Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-1985-0784173-9
- MathSciNet review: 784173