Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1187-1201
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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/
@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},
year = {2001},
volume = {7},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a12/}
}
TY - JOUR
AU - A. V. Strelets
TI - A characterization of operator space modules over full operator algebra
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 2001
SP - 1187
EP - 1201
VL - 7
IS - 4
UR - http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a12/
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ID - FPM_2001_7_4_a12
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%A A. V. Strelets
%T A characterization of operator space modules over full operator algebra
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2001
%P 1187-1201
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%U http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a12/
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%F FPM_2001_7_4_a12
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.
