Cφ和Cφ的数值范围

IF 0.3 Q4 MATHEMATICS
J. Clifford, Michael Dabkowski, Alan D. Wiggins
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引用次数: 0

摘要

本文研究了Hardy空间上C*bφm Caφn和Caφn C*bΦm的数值范围,其中φ是固定原点的内函数,a和b是开单位盘中的点。在|a|=|b|=1的情况下,我们通过构造单位范数的空位多项式来刻画这些算子的数值范围,该多项式的图像在二次形式下递增地叶化数值范围。在a和b都很小的情况下,我们证明了两个算子的数值范围等于限制在三维子空间的算子的数值范围。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Numerical Range of C*ψ Cφ and Cφ C*ψ
Abstract 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.
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
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