Universal Vectors for Operators
on Spaces of Holomorphic functions


Robert M. Gethner and Joel H. Shapiro

Proc. Amer. Math. Soc. 100 (1987), 281--288

Abstract: We give sufficient conditions on a linear operator acting on a topological vector space which insure that the space contains a vector that is universal for the operator, i.e. whose orbit under the operator is dense. Our result applies to the operators of differentiation and translation on the space of entire functions, where it makes contact with Polya's theory of final sets, and also to backward shifts and related operators on various Hilbert and Banach spaces.

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