Strictly Semi-transitive Operator Algebras
نویسنده
چکیده
An algebra A of operators on a Banach space X is called strictly semitransitive if for all non-zero x, y ∈ X there exists an operator A ∈ A such that Ax = y or Ay = x. We show that if A is norm-closed and strictly semi-transitive, then every A-invariant linear subspace is norm-closed. Moreover, LatA is totally and well ordered by reverse inclusion. If X is complex and A is transitive and strictly semitransitive, then A is WOT-dense in L(X). It is also shown that if A is an operator algebra on a complex Banach space with no invariant operator ranges, then A is WOT-dense in L(X). This generalizes a similar result for Hilbert spaces proved by Foiaş.
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