FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

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
```$\mathrm H$
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.

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Last modified: April 17, 2002