Bilateral shorted operators and parallel sums

被引：41
作者：
Antezana, J
Corach, G
Stojanoff, D
机构：
[1] FI UBA, Dept Matemat, RA-1083 Buenos Aires, DF, Argentina
[2] IAM, CONICET, RA-1083 Buenos Aires, DF, Argentina
[3] UNLP, FCE, Dept Matemat, La Plata, Argentina
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 414卷 / 2-3期
关键词：
Schur complements; shorted operators; parallel sum; parallel subtraction; minus order;
D O I：
10.1016/j.laa.2005.10.039
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study shorted operators relative to two different subspaces, for bounded operators on infinite dimensional Hilbert spaces. We define two notions of "complementability" in the sense of Ando for operators, and study the properties of the shorted operators when they can be defined. We use these facts in order to define and study the notions of parallel sum and subtraction, in this Hilbertian context. (c) 2005 Elsevier Inc. All rights reserved.
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收藏
页码：570 / 588
页数：19
相关论文
共 35 条
[1]   PARALLEL SUBTRACTION OF MATRICES [J].
ANDERSON, WN ;
TRAPP, GE ;
DUFFIN, RJ .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1972, 69 (09) :2530-&
[2]   CHARACTERIZATION OF PARALLEL SUBTRACTION [J].
ANDERSON, WN ;
MORLEY, TD ;
TRAPP, GE .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1979, 76 (08) :3599-3601
[3]  
ANDERSON WN, 1975, SIAM J APPL MATH, V28, P60
[4]  
ANDERSON WN, 1971, SIAM J APPL MATH, V20, P520
[5]   GENERALIZED SCHUR COMPLEMENTS [J].
ANDO, T .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1979, 27 (OCT) :173-186
[6]  
BOULDIN R, 1973, TOHOKU MATH J, V25, P359, DOI [DOI 10.2748/TMJ/1178241337, 10.2748/tmj/1178241337]
[7]   A NOTE ON THE SHORTED OPERATOR [J].
BUTLER, CA ;
MORLEY, TD .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1988, 9 (02) :147-155
[8]  
CARLSON D, 1983, LINEAR ALGEBRA APPL, V52-3, P157
[9]   WHAT ARE SCHUR COMPLEMENTS, ANYWAY [J].
CARLSON, D .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1986, 74 :257-275
[10]  
Corach G, 2002, J APPROX THEORY, V117, P189, DOI 10.1006/jith.2002.3696
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