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), 281-288 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), 281-288
- MSC: Primary 47B38; Secondary 30D20, 30H05
- DOI: https://doi.org/10.1090/S0002-9939-1987-0884467-4
- MathSciNet review: 884467