A model for operators with cyclic adjoint

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Abstract

It is proved that every bounded linear operator on a complex Banach space whose adjoint has a w*-cyclic vector, is similar to the differentiation operator on a Banach space of entire functions of finite exponential type. The relation of this model to the existence of non-trivial invariant subspaces is discussed.

Original languageEnglish
Pages (from-to)153-163
Number of pages11
JournalIntegral Equations and Operator Theory
Volume10
Issue number2
DOIs
StatePublished - Mar 1987

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