THE BLOCK NUMERICAL RANGE OF ANALYTIC OPERATOR FUNCTIONS
THE BLOCK NUMERICAL RANGE OF ANALYTIC OPERATOR FUNCTIONS
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DOI：
10.7153/oam-08-51
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发表时间：
2014-12-01
影响因子：
0.5
通讯作者：
Wagenhofer, Markus
中科院分区：
文献类型：
--
作者：
Radl, Agnes;Tretter, Christiane;Wagenhofer, Markus
引入了算子函数L关于分解H=H-1圆+…的块数值范围W-n(L).下层Hilbert空间的圆加H-n。我们的主要结果包括解析L的预解式的谱包含性质和范数估计，它们推广和改进了数值范围(n=1)的相应结果，因为块数值范围包含在通常的数值范围内，并且可能比通常的数值范围小得多。证明了分解的精化包含在相应的块数值值域之间，并且算子矩阵函数L的块数值值域包含其主次子式的块数值值域。对于算子多项式的特殊情况，我们研究了W-n(L)的有界性，并证明了系数在Hilbert格意义下为正的一元算子多项式的块数值半径的Perron-Frobenius型结果。
We introduce the block numerical range W-n (L) of an operator function L with respect to a decomposition H = H-1 circle plus ... circle plus H-n of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L. They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of W-n (L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.