FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 4, PAGES 1187-1201

**A characterization of operator space modules over full operator
algebra**

A. V. Strelets

Abstract

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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 $H$ becomes the left
operator module over
$\$\; \backslash mathcal\; B\; (\backslash mathrm\; H)\; \$$.
Moreover, the corresponding module is contractive if and only if
this Hilbertian is completely isometric to the column one.

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Last modified: April 17, 2002