SOME NEW CLASSES OF COMPLEX SYMMETRIC OPERATORS

被引：156

作者：

Garcia, Stephan Ramon ^{[1
]}

Wogen, Warren R. ^{[2
]}

机构：

[1] Pomona Coll, Dept Math, Claremont, CA 91711 USA

[2] Univ N Carolina, Dept Math, Chapel Hill, NC 27599 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2010年 / 362卷 / 11期

基金：

美国国家科学基金会;

关键词：

Complex symmetric operator; normal operator; binormal operator; nilpotent operator; idempotent; partial isometry;

D O I：

10.1090/S0002-9947-2010-05068-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We say that an operator T is an element of B(H) is complex symmetric if there exists a conjugate-linear, isometric involution C : H -> H so that T = CT*C. We prove that binomial operators, operators that are algebraic of degree two (including all idempotents), and large classes of rank-one perturbations of normal operators are complex symmetric. From an abstract viewpoint, these results explain why the compressed shift and Volterra integration operator are complex symmetric. Finally, we attempt to describe all complex symmetric partial isometries, obtaining the sharpest possible statement given only the data (dim ker T, dim ker T*).

引用

页码：6065 / 6077

页数：13

共 18 条

[1]

Brown A., 1954, AM J MATH, V76, P414, DOI [10.2307/2372582, DOI 10.2307/2372582]

[2] The characteristic function of a complex symmetric contraction [J].