Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-16T19:00:24.135Z Has data issue: false hasContentIssue false
  • English
  • Français

Counterexamples in intersections for C*-tensor products

Published online by Cambridge University Press:  20 January 2009

Seung-Hyeok Kye
Seung-Hyeok Kye
Affiliation:
Department of MathematicsSeoul National UniversityKwanak-Ku, Seoul 151, Korea
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let A and B be C*-algebras and A ⊗ B denote the minimal C*-tensor product of A and B. T. Huruya [1] gave examples of C*-tensor products A ⊗ B with C*-subalgebras A1⊗B2 and A2⊗B2 such that strictly contains , answering a question of S. Wassermann [3, Remark 23]. In this short note, we show that the same situation can occur even if A1 = A2

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 3 , October 1984 , pp. 301 - 302
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Huruya, T., An intersection result for tensor products of C*-algebras, Proc. Amer. Math. Soc. 75 (1979), 186–187.Google Scholar
2.Tomiyama, J.Tensor products and approximation problems of C*-algebras, Publ. Res. Inst. Math. Sci. 11 (1975), 163–183.CrossRefGoogle Scholar
3.Wassermann, S.The slice map problem for C*-algebras, Proc. London Math. Soc. (3) 32 (1976), 537–559.Google Scholar
4.Wassermann, S.On tensor products of certain group C*-algebras, J. Fund. Anal. 23 (1976), 239–254.Google Scholar
5.Wassermann, S.A pathology in the ideal space of L(H)⊗L(H), Indiana Univ. Math. J. 27 (1978), 1011–1020.CrossRefGoogle Scholar