Geodesic
FRAME-LESS HILBERT C*-MODULES
Glasgow mathematical journal, Tome 61 (2019) no. 1, pp. 25-31

Voir la notice de l'article provenant de la source Cambridge University Press

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 $K(\ell^2) \dotplus \mathbb{C}I_{\ell^2}$. 
ASADI, M. B.; FRANK, M.; HASSANPOUR-YAKHDANI, Z. FRAME-LESS HILBERT C*-MODULES. Glasgow mathematical journal, Tome 61 (2019) no. 1, pp. 25-31. doi: 10.1017/S0017089518000010
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     title = {FRAME-LESS {HILBERT} {C*-MODULES}},
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     year = {2019},
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[1] 1. Arambašić, Lj., Another characterization of Hilbert C*-modules over compact operators, J. Math. Anal. Appl. 344 (2) (2008), 735–740. Google Scholar

[2] 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

[3] 3. Arveson, W., An invitation to C*-algebras (Springer, New York, 1976). Google Scholar

[4] 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] 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] 6. Dixmier, J., C*-algebras (North-Holland Publishing Company, Amsterdam - New York - Oxford, 1977). Google Scholar

[7] 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] 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] 9. Li, H., A Hilbert C*-module admitting no frames, Bull. London Math. Soc. 42 (3) (2010), 388–394. Google Scholar

[10] 10. Swan, R. G., Vector bundles and projective modules, Trans. Amer. Math. Soc. 105 (2) (1962), 264–277. Google Scholar

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