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Hyperinvariant subspace for weighted composition operator on Lp

Summary: Hyperinvariant subspace for weighted composition
operator on Lp
([0, 1]d
George Androulakis Antoine Flattot
March 17, 2009
The main result of this paper is the existence of a hyperinvariant subspace of
weighted composition operator Tf = vf on Lp([0, 1]d), (1 p ) when the
weight v is in the class of "generalized polynomials" and the composition map is
a bijective ergodic transform satisfying a given discrepancy estimates. The work is
based on the construction of a functional calculus initiated by Wermer and generalized
by Davie.
AMS 2000 subject classification: Primary- 47A15 ; secondary- 47A10, 47A60.
Keywords: Invariant subspace, weighted composition operator, discrepancy, functional cal-
1 Introduction
We study the existence of invariant (and even hyperinvariant) subspace for weighted com-
position operator on Lp
([0, 1]d


Source: Androulakis, George - Department of Mathematics, University of South Carolina


Collections: Mathematics