INVARIANT SUBSPACES FOR FRECHET SPACES WITHOUT CONTINUOUS NORM

被引：0

作者：

Menet, Quentin ^{[1
]}

机构：

[1] Univ Mons, Dept Math, 20 Pl Parc, B-7000 Mons, Belgium

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 08期

关键词：

Invariant subspaces; Frechet spaces; OPERATOR;

D O I：

10.1090/proc/15418

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (X, (p(j))) be a Frechet space with a Schauder basis and without continuous norm, where (p(j)) is an increasing sequence of seminorms inducing the topology of X. We show that X satisfies the Invariant Subspace Property if and only if there exists j(0) >= 1 such that ker p(j+1) is of finite codimension in ker p(j) for every j >= j(0).

引用

页码：3379 / 3393

页数：15

共 50 条

[31] On the index of invariant subspaces in Hilbert spaces of vector-valued analytic functions
Carlsson, Marcus
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 354 (01) : 184 - 201
[32] Invariant and hyperinvariant subspaces of an operator Jα and related operator algebras in Sobolev spaces
Domanov, IY
Malamud, MM
LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 348 : 209 - 230
[33] Quasiaffinity and invariant subspaces
A. Mello
C. S. Kubrusly
Archiv der Mathematik, 2016, 107 : 173 - 184
[34] Convergence of restarted Krylov subspaces to invariant subspaces
Beattie, C
Embree, M
Rossi, J
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 25 (04) : 1074 - 1109
[35] Quasiaffinity and invariant subspaces
Mello, A.
Kubrusly, C. S.
ARCHIV DER MATHEMATIK, 2016, 107 (02) : 173 - 184
[36] Continuous versions of the Littlewood-Richardson rule, selfadjoint operators, and invariant subspaces
Bercovici, H
Li, WS
Smotzer, T
JOURNAL OF OPERATOR THEORY, 2005, 54 (01) : 69 - 92
[37] Contractions without non-trivial invariant subspaces satisfying a positivity condition
Bhaggy Duggal
In Ho Jeon
In Hyoun Kim
Journal of Inequalities and Applications, 2016
[38] Invariant and hyperinvariant subspaces of the operator Jα in Sobolev spaces Wsp[0,1]
Romashchenko, GS
MATHEMATICAL NOTES, 2003, 74 (1-2) : 147 - 150
[39] Invariant and Hyperinvariant Subspaces of the Operator Jα in Sobolev Spaces Wps[0,1]
G. S. Romashchenko
Mathematical Notes, 2003, 74 : 147 - 150
[40] Diametral dimensions of Frechet spaces
Demeulenaere, Loic
Frerick, Leonhard
Wengenroth, Jochen
STUDIA MATHEMATICA, 2016, 234 (03) : 271 - 280

← 1 2 3 4 5 →