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Universal vectors for operators on spaces of holomorphic functions. (English) Zbl 0618.30031
The authors’ summary: A vector x in a linear topological space X is called universal for a linear operator T on X if the orbit $$\{T^ nx:n>0\}$$ is dense in X. Our main result gives conditions on T and X which guarantee that T will have universal vectors. It applies to the operators of differentiation and translation on the space of entire functions, where it makes contact with Pólya’s theory of final sets; and also to backward shifts and related operators on various Hilbert and Banach spaces.
Reviewer: B.Kjellberg

MSC:
 30D20 Entire functions of one complex variable, general theory
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References:
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