Strictly semi-transitive operator algebras

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An algebra A of operators on a Banach space X is called strictly semi-transitive if for all non-zero x,y in X there exists an operator S in A such that Sx=y or Sy=x. We show that if A is norm-closed and strictly semi-transitive, then every A-invariant linear subspace is norm-closed. Moreover, Lat A is totally and well ordered by reverse inclusion. If X is complex and A is transitive and strictly semi-transitive, 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 Foias.
To appear in Journal of Operator Theory

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Functional Analysis, Operator Algebras, 47A15; 47L10

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http://salesiana.dossiersoluciones.com/handle/123456789/68428

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0309014
 http://arxiv.org/abs/math/0309014

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arXiv