Near-invariant subspaces for matrix groups are nearly invariant

被引：0

作者：

Mastnak, Mitja ^{[1
]}

Omladic, Matjaz ^{[2
,3
]}

Radjavi, Heydar ^{[4
]}

机构：

[1] St Marys Univ, Dept Math, Halifax, NS B3H 3C3, Canada

[2] Inst Math Phys & Mech, Ljubljana, Slovenia

[3] Jozef Stefan Inst, Ljubljana, Slovenia

[4] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2016年 / 505卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Group; Semigroup; Reducibility; Invariant subspaces;

D O I：

10.1016/j.laa.2016.05.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let S be a semigroup of invertible matrices. It is shown that if P is an idempotent matrix of rank and co-rank at least two such that the rank of (1 - P)SP is never more than one for S in S (the range of the kind of P is said to be near-invariant), then S has an invariant subspace within one dimension of the range of P (the kind of range is said to be nearly invariant). (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：269 / 281

页数：13

共 50 条

[31] Invariant Subspaces of Idempotents on Hilbert Spaces [J].

Neeru Bala ;

Nirupam Ghosh ;

Jaydeb Sarkar .

Integral Equations and Operator Theory, 2023, 95

[32] α-FREDHOLM OPERATORS RELATIVE TO INVARIANT SUBSPACES [J].

Sanchez-Perales, S. ;

Palafox, S. ;

Djordjevic, S., V .

OPERATORS AND MATRICES, 2019, 13 (04) :921-936

[33] A new method for constructing invariant subspaces [J].

Androulakis, George .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 333 (02) :1254-1263

[34] Minimal invariant subspaces for composition operators [J].

Gallardo-Gutierrez, Eva A. ;

Gorkin, Pamela .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2011, 95 (03) :245-259

[35] Spectral Continuity Relative to Invariant Subspaces [J].

Sanchez-Perales, Salvador ;

Djordjevic, Slavisa V. .

COMPLEX ANALYSIS AND OPERATOR THEORY, 2017, 11 (04) :927-941

[36] ON A PERTURBATION BOUND FOR INVARIANT SUBSPACES OF MATRICES [J].

Karow, Michael ;

Kressner, Daniel .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2014, 35 (02) :599-618

[37] On the Lipschitz stability of (A, B)-invariant subspaces [J].

Puerta, Ferran ;

Puerta, Xavier .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (01) :182-190

[38] Two Types of Invariant Subspaces in the Polydisc [J].

Koca, Beyaz Basak .

RESULTS IN MATHEMATICS, 2017, 71 (3-4) :1297-1305

[39] Bounded Sequences, Orbits and Invariant Subspaces [J].

Driss Drissi .

Complex Analysis and Operator Theory, 2010, 4 :813-819

[40] INVARIANT AND HYPERINVARIANT SUBSPACES FOR AMENABLE OPERATORS [J].

Shi, Luo Yi ;

Wu, Yu Jing .

JOURNAL OF OPERATOR THEORY, 2013, 69 (01) :87-100

← 1 2 3 4 5 →