FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 1, PAGES 147-159

Property of the spatial projectivity in the class of CSL-algebras with atomic commutant

Ju.O.Golovin

This work continues to study spatial homological properties of, generally speaking, non-selfadjoint, reflexive operator algebras in a Hilbert space H. A "lattice" criterion of spatial projectivity of an algebra A (i.e. the projectivity of H as left Banach A-module) is obtained in the class of indecomposable CSL-algebras: the existence of immediate predesessor of H as element of the lattice of invariant subspaces. Also, the direct product of indecomposable CSL-algebras $A_\alpha$, $\alpha \in \Lambda$, is a spatial projective algebra iff the algebra $A_\alpha$ is spatial projective for every $\alpha$.

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Location: http://mech.math.msu.su/~fpm/eng/95/951/95107.htm
Last modified: October 3, 1997.