This article is cited in 12 papers

Symmetric Banach algebras of operators in a space of type $\Pi_1$

V. S. Shulman


Abstract: We construct a complete system of models of complete $I$-symmetric algebras of operators in a space of type $\Pi_1$, which leave invariant at least one degenerate subspace in $\Pi_1$. The results obtained are applied in the proof of an analog of von Neumann's double commutator theorem, and also in the determination of necessary and sufficient conditions for the reflexivity of weakly closed $I$-symmetric algebras of operators in $\Pi_1$.
Bibliography: 14 titles.

UDC: 519.56

MSC: Primary 46L20; Secondary 46L05

Received: 09.07.1971

 English version: Mathematics of the USSR-Sbornik, 1972, 18:2, 267–283

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