Universal vectors for operators on spaces of holomorphic functions
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 by Robert M. Gethner and Joel H. Shapiro PDF
 Proc. Amer. Math. Soc. 100 (1987), 281288 Request permission
Abstract:
A vector $x$ in a linear topological space $X$ is called universal for a linear operator $T$ on $X$ if the orbit $\{ {T^n}x:n \geq 0\}$ 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.References

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Additional Information
 © Copyright 1987 American Mathematical Society
 Journal: Proc. Amer. Math. Soc. 100 (1987), 281288
 MSC: Primary 47B38; Secondary 30D20, 30H05
 DOI: https://doi.org/10.1090/S00029939198708844674
 MathSciNet review: 884467