On reductive operators and operator algebras

A. I. Loginov, V. S. Shulman


Abstract: We prove a theorem on the structure of weakly closed reductive operator algebras. The proof essentially relies on a known result of V. I. Lomonosov on transitive operator algebras containing a nonzero compact operator. We deduce a number of corollaries which apply to the reductivity problem.
Bibliography: 20 titles.

UDC: 519.4

MSC: Primary 46L15, 47B99; Secondary 46L10

Received: 05.09.1974

 English version: Mathematics of the USSR-Izvestiya, 1976, 10:4, 799–807

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