TOPOLOGICAL PROPERTIES OF THE BLOCK NUMERICAL RANGE OF OPERATOR MATRICES

被引：0
|
作者：
Radl, Agnes [1 ]
Wolff, Manfred P. H. [2 ]
机构：
[1] TU Berlin, Inst Math, Str 17 Juni 136, D-10623 Berlin, Germany
[2] Eberhard Karls Univ Tubingen, Dept Math, Morgenstelle 10, D-72076 Tubingen, Germany
来源：
OPERATORS AND MATRICES | 2020年 / 14卷 / 04期
关键词：
Block numerical range; numerical range; spectrum; resolvent;
D O I：
10.7153/oam-2020-14-62
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the block numerical range of an n x n-operator matrix A corresponding to an operator A on the Banach space X with respect to a decomposition X = Pi X-j has at most n connected components. We then characterize operator matrices with finite block numerical range. As an important tool we prove an inclusion theorem for the block numerical ranges of the principal submatrices of A.
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页码：1001 / 1014
页数：14
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