Multivariable Weighted Composition Operators: Lack of Point Spectrum, and Cyclic Vectors
In the case where a is an irrational vector, we give a new and larger class of weights ω for which the point spectrum of T α,ω is empty. In the case of α∈ℚ d and ω(x 1, ..., x d) = x 1 ...x d, we give a complete characterization of the cyclic vectors of T α,ω.
KeywordsWeighted composition operator Invariant subspace Point spectrum Cyclic vector
Mathematics Subject Classification (2000)Primary: 47A15 47A10 47A16 Secondary: 47B33 47A35
Unable to display preview. Download preview PDF.
- G. Androulakis and A. Flattot. Hyperinvariant subspace for weighted composition operator on L p[0, 1]d). J. Operator Theory, to appear.Google Scholar
- I. Chalendar and J.R. Partington. The cyclic vectors and invariant subspaces of rational Bishop operators. Research report, 2008.Google Scholar
- C.C. Cowen and B.D. MacCluer, Composition operators on spaces of analytic functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1995.Google Scholar
- J.H. Shapiro, Composition operators and classical function theory. Universitext: Tracts in Mathematics. Springer-Verlag, New York, 1993.Google Scholar