Operators with Dense, Invariant, Cyclic Vector Manifolds

Gilles Godefroy and Joel H. Shapiro

J. Functional Analysis 98 (1991), 229--269

Abstract: We study operators patterned after backward shifts, and both adjoint multipliers and differential operators on various spaces of holomorphic functions. We prove that large classes of these operators have very strong cyclic behavior, e.g., many of them are topologically transitive.

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