Displaying similar documents to “The problem of L p -simple spectrum for ergodic group automorphisms”

Subnormal operators, cyclic vectors and reductivity

Béla Nagy (2013)

Studia Mathematica

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Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and *-cyclic vectors, and the equality L²(μ) = P²(μ) for every measure μ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.

Cyclic vectors and invariant subspaces for the backward shift operator

R. G. Douglas, H. S. Shapiro, A. L. Shields (1970)

Annales de l'institut Fourier

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The operator U of multiplication by z on the Hardy space H 2 of square summable power series has been studied by many authors. In this paper we make a similar study of the adjoint operator U * (the “backward shift”). Let K f denote the cyclic subspace generated by f ( f ∈ H 2 ) , that is, the smallest closed subspace of H 2 that contains { U * n f } ( n ≥ 0 ) . If K f = H 2 , then f is called a cyclic vector for U * . Theorem : f is a cyclic vector if and only if there is a function g , meromorphic and of bounded Nevanlinna...