Journal of Operator Theory

Volume 35, Issue 2, Spring 1996 pp. 205-221.

Decomposable weighted rotations on the unit circle

Authors: Gordon W. Macdonald
Author institution:Department of Mathematics and Computer Science, University of Prince Edward Island, Charlottetown, Prince Edward Island, C1A 4P3, CANADA

Summary: Bounds the rate of uniform convergence of Cesáro averages of rotations of functions by a given angle, for certain functions and angles, give norm bounds on the powers of an associated weighted rotation operator. This implies that these operators are decomposable and hence have many non-trivial invariant subspaces. This paper extends the set of rotations for which the associated weighted rotation is decomposable. The case where the function is a characteristic function of an interval is examined in detail, and stronger results are obtained in this case.

Keywords: Invariant subspaces, weighted, rotation, operator, decomposable.

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