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

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

2008-09-25

arxiv.org/abs/0809.4429v1

Mathematics

Functional Analysis

Scientific paper

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.

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