The Numerical Range of C*ψ Cφ and Cφ C*ψ

Concrete Operators

Wiggins Alan¹  Dabkowski Michael¹  Clifford John¹ 

[1] Department of Mathematics and Statistics, University of Michigan-Dearborn, Dearborn, MI, 48128, USA;

关键词: composition operator;    numerical range;    inner function;    weighted shift;    47b33;    47a12;    15a60;   

DOI  :  10.1515/conop-2020-0108

来源: DOAJ

【 摘 要 】

In this paper we investigate the numerical range of C*bφm Caφn and Caφn C*bφm on the Hardy space where φ is an inner function fixing the origin and a and b are points in the open unit disc. In the case when |a| = |b| = 1 we characterize the numerical range of these operators by constructing lacunary polynomials of unit norm whose image under the quadratic form incrementally foliate the numerical range. In the case when a and b are small we show numerical range of both operators is equal to the numerical range of the operator restricted to a 3-dimensional subspace.

【 授权许可】

Unknown