Article contents
FRAME-LESS HILBERT C*-MODULES
Published online by Cambridge University Press: 07 February 2018
Abstract
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.
We show that if A is a compact C*-algebra without identity that has a faithful *-representation in the C*-algebra of all compact operators on a separable Hilbert space and its multiplier algebra admits a minimal central projection p such that pA is infinite-dimensional, then there exists a Hilbert A1-module admitting no frames, where A1 is the unitization of A. In particular, there exists a frame-less Hilbert C*-module over the C*-algebra $K(\ell^2) \dotplus \mathbb{C}I_{\ell^2}$.
MSC classification
Primary:
46L08: $C^*$-modules
- Type
- Research Article
- Information
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 2018
References
REFERENCES
1. Arambašić, Lj., Another characterization of Hilbert C*-modules over compact operators, J. Math. Anal. Appl. 344 (2) (2008), 735–740.Google Scholar
2. Amini, M., Asadi, M. B., Elliott, G. A. and Khosravi, F., Frames in Hilbert C*-modules and Morita equivalent C*-algebras, Glassgow Math. J. 59 (1) (2017), 1–10.Google Scholar
4. Bakić, D. and Guljaš, B., Hilbert C*-modules over C*-algebras of compact operators, Acta Sci. Math. (Szeged) 68 (1–2) (2002), 249–269.Google Scholar
5. Brown, L. G., Complements to various Stone–Weierstrass theorems for C*-algebras and a theorem of Shultz, Comm. Math. Phys. 143 (2) (1992), 405–413.Google Scholar
6. Dixmier, J., C*-algebras (North-Holland Publishing Company, Amsterdam - New York - Oxford, 1977).Google Scholar
7. Elliott, G. A. and Kawamura, K., A Hilbert bundle characterization of Hilbert C*-modules, Trans. Amer. Math. Soc. 360 (9) (2008), 4841–4862.Google Scholar
8. Frank, M. and Larson, D. R., Frames in Hilbert C*-modules and C*-algebras, J. Operator Theory 48 (2) (2000), 273–314.Google Scholar
9. Li, H., A Hilbert C*-module admitting no frames, Bull. London Math. Soc. 42 (3) (2010), 388–394.Google Scholar
10. Swan, R. G., Vector bundles and projective modules, Trans. Amer. Math. Soc. 105 (2) (1962), 264–277.Google Scholar
You have
Access
- 4
- Cited by