Geodesic
A characterization of operator space modules over full operator algebra
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1187-1201

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In the paper it is proved that the column operator structure is the unique one (up to completely isomorphism) such that a given Hilbert space $\mathrm H$ becomes the left operator module over $\mathcal B(\mathrm H)$. Moreover, the corresponding module is contractive if and only if this Hilbertian is completely isometric to the column one. 
@article{FPM_2001_7_4_a12,
     author = {A. V. Strelets},
     title = {A characterization of operator space modules over full operator algebra},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1187--1201},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a12/}
}
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A. V. Strelets. A characterization of operator space modules over full operator algebra. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1187-1201. http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a12/