An intersection result for tensor products of $C^{\ast }$-algebras
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- by Tadasi Huruya
- Proc. Amer. Math. Soc. 75 (1979), 186-187
- DOI: https://doi.org/10.1090/S0002-9939-1979-0529239-0
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Abstract:
There exists a ${C^\ast }$-tensor product $A \otimes B$ with ${C^\ast }$-subalgebras ${A_1} \otimes {B_1}$ and ${A_2} \otimes {B_2}$ such that $({A_1} \otimes {B_1}) \cap ({A_2} \otimes {B_2})$ strictly contains $({A_1} \cap {A_2}) \otimes ({B_1} \cap {B_2})$.References
- Shôichirô Sakai, $C^*$-algebras and $W^*$-algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York-Heidelberg, 1971. MR 0442701
- 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
- Simon Wassermann, The slice map problem for $C^*$-algebras, Proc. London Math. Soc. (3) 32 (1976), no. 3, 537–559. MR 410402, DOI 10.1112/plms/s3-32.3.537
- 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 —, A pathology in the ideal space of $L(H) \otimes L(H)$ (to appear).
Bibliographic Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 186-187
- MSC: Primary 46L05; Secondary 46M05
- DOI: https://doi.org/10.1090/S0002-9939-1979-0529239-0
- MathSciNet review: 529239