Hyperinvariant subspace for weighted composition operator on $L^p([0,1]^d)$

George Androulakis; Antoine Flattot

Hyperinvariant subspace for weighted composition operator on $L^p([0,1]^d)$

Functional Analysis 2008-09-26 v1

Authors: George Androulakis , Antoine Flattot

Abstract

The main result of this paper is the existence of a hyperinvariant subspace of weighted composition operator $Tf=vf\circ\tau$ on $L^p([0,1]^d)$ , ( $1 \leq p \leq \infty$ ) when the weight $v$ is in the class of ``generalized polynomials'' and the composition map is a bijective ergodic transform satisfying a given discrepancy. The work is based on the construction of a functional calculus initiated by Wermer and generalized by Davie.

Keywords

composition operators invariant subspace theory bergman spaces

Cite

@article{arxiv.0809.4429,
  title  = {Hyperinvariant subspace for weighted composition operator on $L^p([0,1]^d)$},
  author = {George Androulakis and Antoine Flattot},
  journal= {arXiv preprint arXiv:0809.4429},
  year   = {2008}
}

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