FPM 2001, vol. 7, no. 4, pp. 1187-1201

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

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