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

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DOI

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
@article{10_1017_S0017089518000010,
     author = {ASADI, M. B. and FRANK, M. and HASSANPOUR-YAKHDANI, Z.},
     title = {FRAME-LESS {HILBERT} {C*-MODULES}},
     journal = {Glasgow mathematical journal},
     pages = {25--31},
     year = {2019},
     volume = {61},
     number = {1},
     doi = {10.1017/S0017089518000010},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000010/}
}
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